Questions about rectangles and its properties.

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-1
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0answers
29 views

How to fit small squares in the big one? [on hold]

Suppose, I have a square S with height H and width W. Also I have another square ...
0
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1answer
12 views

Get the width and height of the inner well aligned rectangle after rotation

I'd like to get the width and height of the red rectangle with this constraints: Maximize the area of the red rectangle The center of the rotation is the center of the original (dotted) rectangle. ...
3
votes
3answers
74 views

How to show that any rectangle in ellipse must be oriented parallel to axes?

A problem which is often given as an exercise for students learning about calculus and finding extrema, is to find maximal possible area of a rectangle inside an ellipse. Such question was asked, for ...
0
votes
0answers
31 views

Approximate area of overlap of two rotated rectangles

I need to estimate the overlap ratio of two rectangles, each one with arbitrary size and orientation. I know how to perform the exact computation, using the Sutherland-Hodgman algorithm, which can be ...
0
votes
1answer
26 views

How big do squares need to be to fit a box, tesselating, with minimal remainder?

A geometry question that I feel utterly defeated by. I'm trying to design a responsive user interface that efficiently fits a variable number of square elements on a screen, by adjusting the size of ...
1
vote
1answer
24 views

Cut corners from rectangle to get box with max volume

I've got a rectangle (no informations about the box, volume box etc.). I need to find how much should I cut from the rectangle to get a box with maximum volume, so I need to find $x = ?$ At the ...
1
vote
1answer
24 views

Consider a rectangle with vertices at E,F,G and H.

Consider a rectangle with vertices at E, F, G and H. Suppose $\overrightarrow{EF}$ = p and $\overrightarrow{FG}$ = q. Express each of the vectors EH, GH, FH and GE in terms of p and q. Hi everybody. ...
2
votes
1answer
26 views

What is the minimum radius $r$ of two intersecting circles that are spaced $x$ apart that completely enclose a square of length $w$?

Let's say we have two circles whose centers are spaced a fixed $x$ units apart from one another. Both circles have a radius $r$. Our goal is to identify the minimum value of $r$ so that the ...
2
votes
2answers
80 views

How do you calculate the area of the intersection between a rectangle and a doughnut?

I'm dealing with an engineering problem, involving concentric pipes, with air flowing through the outer pipe (doughnut). I need a cross-beam to support the inner pipe, so I need to calculate how much ...
0
votes
0answers
17 views

Scale a rectangle about a point considering reflection

Given a rectangle of width $(w_0)$, height $(h_0)$, left $(x_0)$, top $(y_0)$. How do I scale it from an origin $(x_1,y_1)$ with a scale factor of $(w_1, h_1)$ taking into account reflection? This ...
0
votes
1answer
67 views

How can you find the distance between the center and edges of a rectangle - a line from centre to a edge at an angle $\theta$?

I have a case where I know the coordinates $(x,y)$ of the center of the rectangle and its edges where the line is dropped anywhere on the edges $a(x_1,y_1),b(x_2,y_1),c(x_1,y_2),d(x_2,y_2)$. Say I ...
0
votes
1answer
24 views

Area formulae of various shapes

In the definition of perimeter of a shape, we have a very clear view. Perimeter is nothing but the total length of the boundary of a given shape. So formulae for various shapes are also very clear. ...
1
vote
1answer
56 views

Filling a rectangle with 0/1 (constraints on columns/lines sums)

Let's consider a $n \times m$ rectangle wich has to be filled in by $0$s and $1$s. The sum of the values contained in each colum/line is known. Here is an example: This is a solution: Does ...
1
vote
0answers
46 views

Length and width of shadow of rectangular plane

A book that I've read shows how to find the area of the shadow cast by a sphere and ellipsoid. The spherical shadow makes sense; its simply the area of a circle (which would be the sphere's shadow) ...
0
votes
1answer
19 views

The rectangle-partition number and the number of horizontral edges

The rectangle-partition-number of a rectilinear polygon $P$ is the smallest number of pairwise-disjoint axis-parallel rectangles required to cover $P$. Some examples: (in the last example, $P$ is ...
1
vote
3answers
33 views

solving rectangle

Diagonal of a rectangle is $13$ cm. If we extend the length of the rectangle for $4$ cm and width for $7$ cm, then diagonal will be longer for $7$ cm as well. Find sides (length and width) of the ...
0
votes
1answer
90 views

How to divide a large rectangle into N smaller rectangles

I would like to divide a NxMpx rectangle(matrix) into X piece different size smaller rectangles. X is a variable so it dosn't have a fix value.The smaller rectangles must fill the 80-90% area of ...
0
votes
2answers
40 views

Find the sum of the areas of all rectangles whose area is tripled when three units are added to the height and two units are added to the length

A rectangle has all sides of integer length. When three units are added to the height and two units to the length, the area of the rectangle is tripled. What is the sum of all the original areas of ...
1
vote
1answer
63 views

Dimensions of a rectangle containing a rotated rectangle

Given sides a, b, and an arbitrary rotation Θ (0 - 360 degrees) around the centerpoint of the rectangle, how would I calculate sides A and B of a containing rectangle?
0
votes
2answers
52 views

How to keep aspect ratio and position of rectangle inside another rectangle?

This problem has plagued me for many years. Given two rectangles how do I resize the first to fit into the second while preserving the aspect ratio? The second rectangle could be bigger or smaller ...
0
votes
2answers
33 views

Find point on line between two rectangle centers where line hits edge

I have two rectangles as in the picture below which can be located anywhere relative to each other. I have the coordinates of the rectangle centers (c1 and c2) and the lenght/height of both ...
1
vote
2answers
119 views

Can you construct a rectangle with a given side, equal to a square?

In Euclid's Elements, Book 2, Proposition 14, We are shown how to construct a square from a given rectilinear figure. This allows us to square a rectangle. Is it possible to do the inverse, creating ...
0
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1answer
46 views

How to find the value of x given the following rectangular that has been divided into 4 parts?

A rectangle is divided into sections with the area shown. What is the value of X? At first I didn't know what i would do than i noticed that X is 1/4th of the rectangular . But I don't know what to ...
0
votes
2answers
64 views

What is the number of tiles needed to cover a rectangular floor given diagram?

A square tile measures 6 inches by 6 inches. What is the least number of tiles needed to cover a rectangular floor area of 9 feet by 12 feet? So the first thing i tried to do was divide 9 by 6 and ...
1
vote
1answer
39 views

If I have a vector inside a rectangle, how do I tell which side of the rectangle the vector will hit?

I'm trying to solve an issue where I basically have a vector inside of a rectangle. I want to figure out if the vector continues its trajectory, what side will it strike? The vector is given as an (x, ...
0
votes
1answer
51 views

Finding suqares in the rectangle $(0,0,1,1)$ which are “divided with” $\frac{\pi}{4}$ by the unit circle.

I want to write an algorithm which calculates the following: Find all suqares $(x_0,y_0,x_1,y_1)$ which are "in" the suqare $(0,0,1,1)$ and are divided by the unit circle so that their inner area ...
0
votes
1answer
37 views

How to find the angle of a rectangle vertex

before I go further I want you to know that I'm developing a collision detection system in a programming language (Javascript). I'm not used to math terms (it was like 10 years ago when I was in ...
1
vote
2answers
56 views

Question on circles inscribed in a rectangle

In rectangle $ABCD$, $AB = 8$ and $BC = 20$. Let $P$ be a point on $AD$ such that angle $\measuredangle BPC = 90^\circ$. If $r_1, r_2, r_3$ are the radii of the incircles of triangles $APB, BPC$ and ...
1
vote
1answer
25 views

Finding which diagonal area of a rectangle you are in

I am trying to calculate which diagonal half a user has clicked within a box using x and y co-ordinates. I have found out how to do this in one diagonal direction, but can't figure out how to change ...
7
votes
2answers
159 views

Partition of a rectangle into smaller rectangles, with their diagonals forming a loop

The Big and the Small Kingdom are both rectangular islands and divided into rectangular landscape. In each province there is a road that runs along one of the diagonals. On each island exist roads ...
0
votes
1answer
154 views

Find points of Rectangle given two diagonal points and a normal in 3D

I'm developing a geometry framework in a program I'm working on that contains all the good stuff like vectors, points, lines, planes, polygons, etc. I was attempting to create a rectangle object, but ...
0
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0answers
7 views

Moving overlapping rectangle by a vector portion

I have rectangles: $S$, $T$, and $R$, described by their top left and bottom right corners, such as $S = ([S_{x1},S_{y1}], [S_{x2},S_{y2}]$), etc. The rectangles $S$ and $T$ are connected by a line ...
1
vote
1answer
10 views

Prove that a polyrectangle in an open set has a superset polyrectangle.

Theorem: Let $S \subseteq \mathbb{R}^n$ be an open set. Let $P \subset S$ be a polyrectangle. Then there exists another polyrectangle $P'$ such that $P \subset P' \subset S$. A ...
3
votes
4answers
722 views

How do I find the maximum perimeter of a rectangle inscribed in an ellipse?

The problem I've been stuck on is this: A rectangle is inscribed in the ellipse $$\frac{x^2}{20} + \frac{y^2}{12} = 1$$ What is the maximum perimeter of the rectangle? I don't even know if I'm ...
0
votes
2answers
91 views

Scale a rectangle from a point other than its center [closed]

How do I scale a rectangle from a point other than the centre of the rectangle? Specifically, I am trying to determine the new X and Y position of a rectangle after having rescaled it, taking into ...
1
vote
0answers
47 views

Filling a rectangle with congruent squares in two columns

I have a rectangle. This rectangle is divided into two columns; the widths of these columns are not necessarily equal, and are not known. I want to fill the rectangle with squares. The number of ...
18
votes
2answers
250 views

Largest rectangle not touching any rock in a square field

You want to build a rectangular house with a maximal area. You are offered a square field of area 1, on which you plan to build the house. The problem is, there are $n$ rocks scattered in unknown ...
0
votes
0answers
66 views

Determine what is length and what is width of a rectangle

I have an algorithm to write for an app. So I am given a reference rectangle with known width and length and I have bigger rectangle which sides I have to determine, where one side is known. I realize ...
2
votes
1answer
39 views

Covering a rectangle with circles

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-4
votes
1answer
41 views

How to find whether a rectangular keyboard can fit into a square bag? [closed]

Will a 18.6'' x 1.3'' x 6.8'' keyboard fit into a 15''x15'' bag? If yes, how will it have to be oriented? If no, what size bag would I need for the keyboard to fit? What I have figured already is ...
0
votes
1answer
26 views

Is this Quadrilateral possible?

Is this figure possible to achieve? $AD > BC$; $\angle BCD$ = $\angle BAD$ = $90^{\circ}$ . And this is supposed to be a closed quadrilateral. I'm confused as to whether this is viable - since ...
0
votes
3answers
57 views

How Does the Area of a Rectangle Work?

I understand the formula that the two sides must be multiplied, but what is the reason for this? I think of area as the space an enclosed figure occupies in a two-dimensional plane. It seems to me ...
1
vote
2answers
62 views

How to prove three points are collinear when constructing a rectangle

My problem is: Choose a unit segment OI. Then construct a rectangle with base 3 units and height 2 units. I cannot use angle measure. I know I can construct this figure from my unit segment by using ...
1
vote
3answers
180 views

To find ratio of Length and Breadth of a Rectangle [closed]

Given a rectangular paper sheet. The diagonal vertices of the sheet are brought together and folded so that a line (mark) is formed on the sheet. If this mark length is same as the length of the ...
-2
votes
1answer
80 views

Find the length of rectangular field given its area and ratio of sides [closed]

The area of a rectangular field is 9,000 square meters. If the ratio of the width to the length is 5 is to 8, what is the length of the rectangular field in meters?
3
votes
3answers
179 views

Check if a point is inside a rectangular shaped area (3D)?

I am having a hard time figuring out if a 3D point lies in a cuboid (like the one in the picture below). I found a lot of examples to check if a point lies inside a rectangle in a 2D space for example ...
0
votes
1answer
108 views

Proofs involving triangles and rectangles

The figure below represents a rectangle ACLK with an inscribed right triangle ABC. The lower case letters represent lengths of segments (ex. x=|KB|, etc. a.) prove that triangle ABC is similar to ...
0
votes
0answers
102 views

Finding angle for rotated rectangles

I need to find the rotation angle for rectangles that always have the same aspect ratio and are defined by points $r_0, r_1, r_2$ and $r_3$. The points are always in clockwise order and the rectangle ...
0
votes
0answers
21 views

Area of Rectangle stretched from corners?

If the corners of a 3-inch by 4-inch rectangular photograph were stretched uniformly by 1.5-inch, what would be the area in square inches, of the enlarged rectangular photograph?
0
votes
1answer
88 views

Give a coordinate proof that a parallelogram is a rectangle iff its diagonals are congruent

I'm kind of confused on how to solve this one, especially through using coordinate proof. I know how to prove the other way around. If you know that you have a rectangle, then you know that it's ...