Questions tagged [rectangles]
Questions about rectangles and their properties.
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Area of a right angled triangle given the dimensions of an inscribed rectangle
Is there a way to find the area of the right-angled triangle given the dimensions of the rectangle? The rectangle can fit into the same right-angled triangle in two ways, as shown below:
Let $a$ = ...
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Maximize rabbit pen size (no calc) [duplicate]
Question:
To make an enclosure for your pet rabbits, you want to fence a rectangular pen against your house. Only 3 sides will need to be fenced. You have 170 feet of fencing material, and want to ...
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Value of angles of a quadrilateral [closed]
$ABCD$ is a rectangle, $\overline{AC}$ and $\overline{BD}$ are its two diagonals, $O$ their intersection point, and $\angle COD=68^{\circ}$. What is the value of $\angle (BAO-OBC)$?
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Prove some results in a cube...
Question
Let $ABCDA'B'C'D'$ be a cube and the points $M, N, Q$ the means of the sides $A'B', A'D', DC$. We denote by $\alpha=(MNQ)$.
a) If the line $D'C'$ intersects the plane $\alpha$ at the point $T$...
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Is this a new point on the nine-point-circle of a triangle?
I was trying to get a feel for how to solve another question about the largest triangle that can fit in a unit square, by constructing the smallest enclosing square of a triangle in Geogebra. While ...
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Find all possible values of the perimeter of a rectangle with sides $x, y \in \mathbb{Z}^+$, where its area is given by $A=3x+3y+\sqrt{9x^2+9y^2}$
Find all possible values of the perimeter of a rectangle with sides positive integers $x$ and $y$ where its area is given by $A=3x+3y+\sqrt{9x^2+9y^2}$
In other words if $xy=3x+3y+\sqrt{9x^2+9y^2}$, ...
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Longest line in a rectangle [closed]
Given a rectangle, how can one show that the euclidian distance between any two points inside the rectangle (or on its borderies) is smaller or equal than the distance of the diagonal of that ...
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Geometry inequality question (picture attached) [closed]
This question is from a mock test of GRE Quant section. Unfortunately, they only provided the answer key without explanation.
The question asks:
Quantity $A = a + b$
Vs.
Quantity $B = 200 - c$
Which ...
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Help me understand the answers
THE PROBLEM
Let $ABCD$ be a rectangle and $E, F$ the means of the sides $AB$, respectively $AD.$ We know that there is a point $M$ on the segment $AC$ such that $\angle EMF = 60$ and $AC^2 = 4*ME*MF$ ...
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Proving that no tile can fill both squares and equilateral triangles
Cut up a square into a finite number of identical tiles.
Here is one possibility:
How do I prove that the tiles could never be rearranged to form an equilateral triangle (with filled interior and no ...
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How can I check if a rotated rect intersects a non-rotated rectangle?
I have a rotated retangle and a rectangle. Both are defined by their corners (however, for the non-rotated ones I also have access to topLeft, topRight, etc).
Is there a way I can check if they ...
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Find an angle in a rectangle. [closed]
A few days ago, I came across a problem that has driving me insane. It seems so simple, but I just can't solve it, it's like a blind spot to me. Here's the problem:
A point $N$ is taken on the side $...
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Finding safe points in polygons
Let $P$ be an axes-parallel polygon. A point $(x,y)\in P$ is called safe if for any pair $d_x\in[0,1],d_y\in[0,1]$, either $(x+d_x,y+d_y)$ or $(x-d_x, y-d_y)$ or both are in $P$.
Figuratively, suppose ...
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What pair of rectangle shapes is exchanged by cutting off a square?
What pair of rectangle shapes is exchanged by cutting off a square?
According to https://oeis.org/A059966 the golden rectangle has period one when cutting off a square. What pair of rectangle (shapes)...
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Parallel lines passing through rectangle angles
I have a rectangle (side length L1 and L2) and two parallel lines passing through two opposite angles:
(sorry the image is missing due to stackexchange policy)
I know that the (perpendicular) distance ...
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You have $n$ rectangles of area $1$ (and variable height). Pack as many as possible in a semicircle of area $n$. How many leftovers will there be?
You have $n$ rectangles of area $1$ (and variable height). Pack as many of these rectangles as possible in a semicircle of area $n$. How many leftover rectangles will there be, in terms of $n$?
How to ...
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How to calculate dispersion measure for a set of rectangles?
I want to calculate the dispersion measure of a set of rectangle(30) in such a way that the rotation is considered in the calculation. All the rectangles have same dimension. A rectangle $r_i$ is ...
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What is the distance between the centres of two touching rectangles?
What is the distance between the centres of the two rectangles shown in the image?
This distance should be expressed in terms of the lengths of the sides of the rectangles and the angle $\alpha$ in ...
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How to round output rectangles of SquarifiedTreemap algorithm so they can fit a grid with every tile being 1x1
This can be trivial but nonetheless I need help... :)
I have a grid, every tile of the grid is 1x1. I'm using SquarifiedTreemap algorithm to divide the grid in rooms, but the result values are in ...
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How to calculate similarity between two rectangles?
How to find similarity between two rotated rectangles, while considering the rotational symmetry into account?
Assume we have two 2D rectangles of same dimension rotated around the center, $R_a$ and $...
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Cutting a rectangular piece from a right triangle
A piece of sheet metal has the shape of an acute right-angled triangle AB with side BC and height AA' each having 12 cm. From it, a rectangle with two vertices is cut on the base BC and the other two ...
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Questions about ratio and overlapping figures
As I am helping my younger brother on his math papers (bought on external sources), I came across a question that seems unsolvable.
I feel that the question is not complete as they did not state the ...
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How to determine the maximum area of a rectangle in a coordinate system with a function?
I am currently struggling with a math problem and was wondering if someone could help me out. The problem is as follows:
In a coordinate system, a rectangle is drawn with one corner at the origin, one ...
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Find polygon after translate/cut process, starting from rectangle
I have a geometrical question, but if need be I mention that I use Qt so I can do some cool geometric stuff if needed, like QPolygon::intersected(QPolygon)
For more ...
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Find the number of points inside a rectangle if the rectangle is divided into $210$ triangles.
A number of points is drawn inside a rectangle. The rectangle is divided into 210 triangles whose vertices coincide with the vertices of the rectangle and/or the points drawn inside the rectangle. ...
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Geometry of a rectangle and a semi circle [closed]
Given a rectangle $ABCD$ where $AB=|2a|$ and $BC= |\sqrt2a|$. On the side of $AB$, as a diameter, a semi-circle is constructed externally. Let $M$ be an arbitrary point on the semi-circle, the line $...
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$S$ and $Q$ are situated in opposite regions with respect to $PR$ in $\triangle PQR$ ,What is the length of $QS$?
I am currently working on an Olympiad math problem, and I am struggling to find a solution. I would greatly appreciate your help in solving this problem. I was unable to solve the problem because I ...
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Find the position of a rectangle that touches a given circle when the direction of the line joining their centres are known.
I have a rectangle, the sides of which are parallel to $x\text{-}$ and $y\text{-axis}$. The length of the sides are known, i.e., width = $W$ and height = $H$. I also have a circle of radius $R$ with ...
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number of subrectangles
I have a square matrix generated by a cyclic shift of a vector which contains only 0's and 1's. For example,
$$
\begin{matrix}
1 \; 1 \; 0 \; 1 \; 1 \\
1 \; 1 \; 1 \; 0 \; 1 \\
1 \; 1 \; 1 \; 1 \; 0 \\...
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I couldn't understand the last part of the argument. Why is the length of a side in a 4 sided stuff proportional to angle?
Why is DE =3?
I don't quite get it. What theorem did he use?
https://www.youtube.com/watch?v=Dk9mfrIL7FQ
I also don't understand why all four corners of a four sided object is in a circle if the sum ...
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Squeezing a convex shape between two squares
You are given a convex shape $S$ in the plane. You are allowed to apply any affine transformation to $S$. Then, you have to pick an axes-parallel square contained in (the transformed) $S$, and an axes-...
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How many circles of radius R with a D distance between them, fit in rectangle of B x L
i have a rectangle of B x L meters and i want to know how many circles with R radius can fit if there is a space of D between them. All the values wil be integers always.
I tried this.
With this ...
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Are "rectangle" subsets of a flat torus exactly the products of connected sets?
I think the following statement on flat-tori is true, but I feel uncertain and am thus posting as a sanity check:
First the convetions I am using:
The $1$-torus is the quotient space $\mathbb{T}^1 := ...
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Hyperplane Separation Theorem for non-axis aligned rectangles?
I'm trying to understand how the Hyperplane Separation Theorem works.
I found a function on MATLAB that implements it, accepting the parameters
rect1 = [0 0; -1 3; 6 4; 7 1];
rect2 = [12 0; 14 1; 13 ...
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A function to transform a rectangle into a triangle and vice versa.
I have two input variables, let's call them x and y, which are the inputs to a function. There is a condition for these two inputs: x+y must be equal to or less than 1. So, my input space would look ...
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Is the converse of Vertically opposite angles true?
When two straight lines intersect the vertically opposite angles are equal.
But, can we say that, if the vertically opposite angles of two lines are equal then the lines are straight?
The angles ...
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how many rectangles in a circle with defined measurements
example of rectangles in circle
i have various size plates as follows
12m
10m
8m
6m
4m
i need to be able to calculate how many rectangles i need in a quardrant(can be mirrored for other quadrants)
the ...
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Proof of the equation for a rectangle in the Cartesian coordinate system with distances and absolute values [closed]
Can anyone help me find an approach to deriving the equation
$$
\left\lvert \frac{x}{p}+\frac{y}{q} \right\rvert + \left\lvert \frac{x}{p}-\frac{y}{q} \right\rvert = c
$$
for a rectangle in the ...
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Align end of lines of ellipse on top of rectangle border
I know the question includes source code but the problem itself is purely mathematical, so maybe this is the right place anyway
I have the following code to draw circles, squares, ellipses and (wrong) ...
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Finding area of rectangle with height 'x' enclosed within triangle of height 'h' and base 'b'
A rectangle with a height x is drawn with its base lying on the base of the triangle. The triangle has an altitude with height h and the length of its base is b. How can I calculate the area of the ...
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How can I write a single function expression describing some ellipses in a rectangular domain?
I have a rectangular domain (0<x<a, 0<y<b) and have some filled cylinders with ellipse cross-sections and different sizes which are located separately within this domain. How can I write a ...
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How many rectangles can be found in a 5 x 5 square? Diagonal rectangles are allowed.
In a 5 x 5 square, there are 225 rectangles, but what if I allow for rectangles that are diagonal? How many more rectangles would I have? Here is an example of a diagonal rectangle:
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The average distance from the centre of a square or rectangle to a point within this shape
I know that for a circle, the average distance from the center to a point is $(2/3)\sqrt{A/pi}$ in which A is the surface of the circle. This is understandable for me. However, I am wondering about a ...
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Calculate the maximum rotation angle of a rectangle to overlap a smaller rectangle within a fixed distance
I'm trying to figure out how far a rectangle can rotate from its center while still overlapping a smaller rectangle given vertical and horizontal constraints
Rectangle overlap without rotation
...
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Calculate the radius of rectangle corner
TL;DR - rx = |x1-x0|; ry = |y1-y0|; is the formula for figuring out the radius of a rounded rectangle corner. It works with the first set of data but not the second. Why?
I need to calculate the ...
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Find the area of the shaded region in the diagram, in terms of $\theta$
Problem
A company is designing a new logo. The logo is created by removing two equal segments from a rectangle, as shown in the following diagram
The rectangle measures $5cm$ by $4cm$. The points $A$ ...
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Arrange N unit squares in form of a grid such that number of rectangle is maximum?
You are given N square tiles of dimension 1×1. You have to arrange them in form of a grid such that total number of rectangle (of all possible dimensions) is maximum.
Hollows within the grid are not ...
user1057393
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Can a circle be drawn to pass through a point and contain a rectangle?
Let $a, b, c, d$ be points in the Euclidean plane. Suppose that $abcd$ is a non-degenerate rectangle, and that the length of the line segment $ab$ is at least as big as the length of the line segment $...
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Guessing rectangle hypotenuse angle from proportion between it's sides
if a rectangle has it's width as double it's height, can I assume that his hypotenuse will divide the his angle in a proportion of 2:1, or as the angle is 90, the angles would be divided so one part ...
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Evenly skewing a rectangle (= turning it into a trapezoid): Calculating the length of the base
I have a basic rectangle, which I want to skew to give the illusion of perspective (I'm creating a Python program). Here's what I mean. The angles in the picture are just exemplary; I want this to be ...
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