Questions tagged [rectangles]

Questions about rectangles and their properties.

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2
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1answer
42 views

Finding points of 3D non-axis aligned box from min/max and angle

From the graphic depicted in this question: Check if a point is inside a rectangular shaped area (3D)? Points $P_1$ and $P_7$ are known. They are opposite corners of the box. I can obtain Min/Max with ...
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1answer
14 views

Finding remaining 4 points of Cuboid

Starting with points $P_1, P_2, P_4, P_5$ of a Cuboid from the graphic seen in this Question: Check if a point is inside a rectangular shaped area (3D)? How do I find the remaining points $P_3, P_6, ...
2
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1answer
49 views

Calculate minimum horizontal distance to avoid overlap when rotating adjacent rectangles

I have two equally sized rectangles $(2$m $\times$ $1$m$)$ adjacent to each other. When both rectangles are rotated around their centre point, they can overlap, for example at $50$ degrees: Knowing ...
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1answer
34 views

Means of neighboring squares

mn squares of equal size are arranged to form a rectangle of dimension m by n where m and n are natural numbers. Two squares will be called 'neighbours' if they have exactly one common side. A natural ...
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2answers
62 views

Rectangle Inscribed in Triangle

Let $\triangle ABC$ be an isosceles triangle with base $a$ and altitude to the base $b.$ I am trying to find the sides of the rectangle inscribed in $\triangle ABC$ if its diagonals are parallel to ...
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0answers
73 views

Euler's Theorem and Rectangles

A rectangle is divided into smaller rectangles, whose sides are parallel with the big rectangle. Let $x$ be how many intersections there are (a point in the interior where $4$ rectangles meet), $y$ ...
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1answer
41 views

Which area is more fundamental: parallelogram or triangle?

After years of studying math, I still have this basic question. I learned areas of square, triangle, and others as they are by listening to what was told in elementary school. However, I then know a ...
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3answers
36 views

Write an equation for the perimeter of a rectangle and solve for $x$ given dimensions and perimeter

I found an interesting math problem. The perimeter of rectangle is 24 cm, and its dimensions are 2/x and 5/(x+1). Form an equation and find the value of x. I got stuck with 2 values of x: x=-2/3 or x=...
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1answer
21 views

Area of a rectangle using congruency

I don't understand the lecturer, solving the question, says that the rectangles are congruent each other, so the result can be obtained by proportioning them to each other. However, AFAIK two ...
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5answers
728 views

How to find area of rectangle inscribed in ellipse.

In an ellipse $4x^2+9y^2=144$ inscribed is a rectangle whose vertices lies on the ellipse and whose sides are parallel with the ellipse axis. Longer side which is parallel to major axis, relates to ...
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0answers
9 views

Is there a partition $P$ of $A$ such that any subrectangle of $P$ is included in some $U_i$?

Let $A \subset \mathbb{R}^n$ be a closed rectangle. Let $U_1, \cdots, U_m$ be an open cover of $A$. Then, is there a partition $P$ of $A$ such that any subrectangle of $P$ is included in some $U_i$...
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1answer
36 views

Finding the diagonal of a rectangle.

What fraction of the rectangle is shaded? (You may assume that each line, other than the diagonal of the rectangle, is parallel to some side of the rectangle.) Is there a way to solve this without ...
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1answer
100 views

How many whole rectangles can you catch in a grid?

There are $n$ rectangles packed in a square; all of them are axes-parallel. You are allowed to partition the square into a grid of cells, with $1$ or more rows and $1$ or more columns. You score a ...
2
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1answer
77 views

determining the number of equable hyperrectangles with positive integer lengths and a given number of dimensions

Two dimensional equable shapes are those shapes whose area and perimeter are numerically equal. There are only two rectangles that have the numerical equivalent of area and perimeter with positive ...
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0answers
21 views

Solve a Laplace Boundary Value Problem

This is the easiest example from the book, but in the book everything is showed. So how would you solve this problem if you got it on a exam. I dont understand how to solve for $y$ after getting $x$. ...
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1answer
22 views

Scale Rectangle B so that it covers rectangle A at any rotation

this is my first post on this site and I'm not a mathematician so forgive me if I don't use the right terminology. I have two rectangles (let's say they're squares to make it easier, so a 1:1 aspect ...
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1answer
35 views

Maximum number of subrectangles that lie completely within a rectangle

Suppose I have $n$ rectangles in the 2D plane, as shown on the left. I am interested in partitioning the region inside these rectangles into disjoint sub-rectangles and counting the number of ...
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1answer
67 views

Rectangle $ABCD$: prove $XA ^ 2 + XC ^ 2 = XB ^ 2 + XD ^ 2$ for any space point $X $. [closed]

Given the rectangle $ABCD$, prove that for any point $X$ of space the equality $XA ^ 2 + XC ^ 2 = XB ^ 2 + XD ^ 2$ is fulfilled.
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1answer
21 views

Centroid coordinates of an irregular quadrilateral within a rectangular plane

I am developing a robotic project; the robot moves within a rectangular area 80cm x 180cm on a level horizontal surface. The area is bounded by four vertical walls, the robot has onboard four ultra-...
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0answers
11 views

How to track Top Left position of rectangle when scaling from center of pages.

I am building some drawing apps that require to track the XY coordinate of user drawing rectangle (it can be multiple rectangle) on image. Now i have bump into a problem is i do not know how to track ...
2
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2answers
71 views

What’s the average length of chords at a given angle in a rectangle?

Articles are published on average length of chords on circles, squares, rectangles etc..like [1] where they considered either random chords or chords at all angles in a regular geometry, but I could ...
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1answer
37 views

Finding distance of a vertices of a rectangle from another point in it when distances to other three vertices is given.

Let $X$ be a point inside a rectangle $ABCD$. If $XA=a$, $XB=b$, $XC=c$. Find $XD$. I tried by using cosine rule on all the triangle formed and equating what I got. Then I tried to find the ...
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1answer
23 views

Is it possible to find the dimensions of a rectangle from the inner radius and the diagonal?

It seems that given the variables length, width, area, perimeter, diagonal length, outer radius,inner radius of a rectangle, it is (almost)possible to get every other variable if any pair of said ...
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1answer
64 views

How to find the dimensions of a rectangle given a) the area and the diagonal or b) the perimeter and the diagonal

I need to write concise formulas of these two:$\space \space \space$ $(1)$ finding the dimensions of a rectangle given the Area and the diagonal $\space \space \space$$(2)$ finding the dimensions of a ...
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1answer
16 views

What’s the formula for finding the sides of a rectangle given Area and Perimeter [closed]

I have been trying to figure this out for some time now and I managed to find some videos on google of them solving the problem with certain values, but I need to write down a concise formula with ...
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1answer
22 views

Area of rectangle of the following image [closed]

With the right triangle EMT has 5,12, and 13 of length. Any help would be appreciated
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2answers
36 views

Taylor series to approximate a nonlinear problem to a linear problem

How do I convert the function $f(x,y) = xy$ (area of a rectangle) to a linear function using Taylor Series? My attempt at this is as follows (please tell me if I am right/wrong: $L(x,y) = f(a,b) + ...
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4answers
57 views

Right Triangle Within a Rectangle, Hypotenuse Shares Entire Side of Rectangle and Third Point Intersects Rectangle Opposite Side

I know the Length (L) and Width (W) of a rectangle is 8 and 3.5 meters respectively. Triangle ABL is a right triangle, therefore angle AB is 90-degrees. L = C + D = 8 W will fall within this range: ...
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1answer
38 views

Right-triangle, prove $cxy=v^3$

In the right-triangle $\Delta ABC\;(\measuredangle BCA=90^{\circ})$ $\overline{CD}\;(|CD|=v)$ is the altitude on the edge $\overline{AB}\;(|AB|=c)$. $x$ and $y$ are perpendicular to the edges $\...
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1answer
86 views

Proof that you can approximate any continuous function using rectangles/step functions within a small error

Proof that rectangles or a combination of step functions can approximate any continuous function within a small $\epsilon$ which represents the error between the approximate step function and ...
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1answer
45 views

What's the length of $EG$ in terms of $AB$ and $BC$?

By drawing the angle bisectors of a parallelogram, they intersect in points $E,F,G,H$ and the quadrilateral $EFGH$ is formed. It can be proven that $EFGH$ is a rectangle؛ But I've struggled with ...
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1answer
34 views

Why does point $A=(a,b)$ with $a$ and $b$ varying from $-10$ to $+10$ follow a rectangular path on the graphing calculator?

Let $A$ be the " moving" point $(a,b)$ with $a$ and $b$ two variable coordinates ranging from $-10$ to $+10$, with equal rhythm of change. When I create this point on a graphing calculator, I ...
2
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1answer
38 views

Angle between diagonals of a rectangle

I have both of an rectangle and want to find angle between diagonals of a rectangle (angles α, β) I've found the following Math ...
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0answers
34 views

Calculating whitespace given list of rectangles?

It's part of a software application, but should be irrelevant for this. The main thing is the code generates a set of rectangles (with each having x, y position and width, height). Some rectangles ...
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1answer
31 views

quotient top., continuous and bijective map

Let $A = [0,1] \times [0,1]$. Let $B = A \setminus_{\sim}$, where $\sim$ is generated by $(t,0) \sim (t,1) \ \forall t \text{ and } (0,s) \sim (1,s) \ \forall s$. Consider further $S^1 \times S^1 = \...
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1answer
28 views

What is the eccentricity of the ellipse?

Given, Ratio of Area of rectangle formed by end points of L.R to that of ellipse is $ \frac{1}{\pi} $. Therefore, Area of rectangle $A_1$ = Distance between focii × Length of L.R $A_1 = (2ae)(\frac{...
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1answer
39 views

Number of rectangles on a chessboard with restrictions

Number of rectangles on a chessboard with restrictions Suppose there is a $m*n$ chessboard. This implies that there are $m+1$ horizontal lines and $n+1$ vertical lines. If I wanted to count the ...
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0answers
84 views

Term for a rectangle-like arrangement of three line segments

Is there a proper geometric term for the class of line arrangement demonstrated here? i.e. rectangles with one edge missing, or put differently, any rectilinear arrangements of three segments.
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1answer
41 views

Length of an line segment extended from triangle inscribed in rectangle

I have solved the first two problems (1 and 2.1) but 2.2 is giving me trouble. I am able to find some lengths but just come up empty when trying to find the actual answer. If anyone could help me I ...
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5answers
150 views

Possibility of finding exact value of circle area

I am taking a Calculus course and my current theme is calculating a circle's area from scratch, and the tutor is splitting the circle in smaller circle shapes, draws them as a rectangle and putting ...
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1answer
70 views

Why are those the Borel sets?

I have read several definitions and examples, but I still don't understand the Borel-sets clearly. I found the following: Let $(X,\mathcal{T})$ a topological space. We say $\sigma(\mathcal{T})$ ...
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1answer
29 views

I have a rectangle with dimensions of 5x2.5 cm, how big of a circle do I need in order to fit that rectangle in the top part of the circle

I have a rectangle with width of 5 cm and height of 2.5cm and I am wondering how big of a circle do I need in order to fit that rectangle in the top part of the circle like I've shown in the image ...
5
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1answer
792 views

“Cuboid” not the correct name for 3d rectangle?

I have always thought the best name of the 3d equivalent of a rectangle was "cuboid". I am talking about the 3d shape with 6 rectangular faces shown below. However, when looking up the name of this ...
2
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1answer
139 views

Finding the area enclosed by the locus of the vertex of the rectangle at which the normals meet.

Let a and b be the lengths of the semimajor and semiminor axes of an ellipse respectively. Draw a rectangle whose two sides are tangent to the ellipse and the other two are normal to the ellipse. I ...
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2answers
48 views

Find x in this image

The two of 1/4 circles with radius r are fitted in a rectangle with one of the sides a. Find another side x.
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2answers
65 views

Maximum length of a rectangle given a fixed container size

I have a rectangular container with sides A,B. I have a second rectangle with sides C,?? Side ?? should be the largest length possible while still remaining inside rectangle A,B. I need to create and ...
0
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1answer
41 views

how to find overlapping areas of a circle and triangle

I was asked in my calculus class to find the blue areas, two of which are overlapping with a circle and one of which is a part of a semi circle, I was given the equation of a circle $\ x^2+y^2 = r^2$, ...
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4answers
99 views

How to find the overlapping area of a semicircle and a rectangle

I am being asked to calculate the pink area that is overlapping between the semicircle and the rectangle. I was only given the radius of the circle (5), the equation of a circle $(x^2+y^2 = r^2).$ I ...
0
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1answer
41 views

Place (Scatter) random rectangles in a bigger rectangle

I am making a voxel game and creating the terrain, The ground and elements on it are rectangles, First of all I want to generate the elements guaranteed that their total area is less than ground ...
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1answer
72 views

proving fractional Helly's theorem for boxes and rectangles

I'm having a hard time proving the followings. the background: I'm self-learning combinatorial geometry based on 'lectures on Discrete Geometry' by Matousek: Q1.Let B be a finite family of axis-...

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