Questions about rectangles and its properties.

learn more… | top users | synonyms

1
vote
3answers
29 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
14 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
25 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
34 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
26 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
26 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
56 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
votes
1answer
24 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
28 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
33 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
49 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
16 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
52 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
20 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
131 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
77 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
votes
0answers
5 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
9 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
385 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
38 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
31 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
225 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
34 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
30 views

Covering a rectangle with circles

On a rectangle table with area A, n unit-radius circles are placed and it is not possible to place any extra circles without overlapping with some of the existing ones or without placing circle's ...
-4
votes
1answer
39 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
24 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
0answers
28 views

How to cut out a rectangle from a sphere

Given a sphere, I'd like to cut out a rectangle out of it. How can I do it using spherical coordinates if I know the position of the centre of that rectangle?
0
votes
3answers
46 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
42 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
86 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
45 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
84 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
83 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
67 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
18 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
65 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 ...
0
votes
1answer
23 views

Have a doubt about few concepts - Can anyone elaborate it

For a given perimeter, the rectangle with the largest area is a square. For a given area, the rectangle with the smallest perimeter is a square. What do the above sentences mean? Can any one explain ...
0
votes
1answer
81 views

what's the greatest volume of a cylinder using calculus?

I have a rectangle that has the perimeter of 38cm. I need to make this rectangle into a baseless cylinder and find the greatest volume of it, by deriving. so far i came with this: for the rectangle ...
1
vote
1answer
50 views

How to calculate optimal sizes of rectangles for this type of array visualization?

Given array of positive numbers, I would like to draw this diagram and be able to put descriptions inside: There should be no empty space left, consider that these numbers represent % of total. Do ...
1
vote
1answer
60 views

Finding the mid-point of the line between two rectangle centers from edges. [closed]

In the image there are 4 rectangles, each rectangle has a center-point and 4 edges. So I'm trying to figure out how to create a line from the center of one rectangle to the center of another ...
1
vote
1answer
78 views

Finding the area of an open rectangular tank

I tried approaching this as a normal rectangle, but my answer doesn't seem to be in the options. Here's the question - An open rectangular tank: 4m long, 3m wide and 4m high is made out of a thin ...
2
votes
2answers
46 views

Covering rectangle with tiles

Bottom of rectangular box (which is obviously a rectangle) is covered by $2*2$ and $1*4$ tiles. Tiles were removed out of the box and shuffled. One $2*2$ tile was lost. We replaced it with $1*4$ tile. ...
0
votes
1answer
47 views

Find the Angle of a Rectangle's Diagonal

For a geometric rectangle with arbitrary sides of length $a$, $b$, and $c$. The following are known: $\theta$ where $\frac ac = \tan\theta$ $\phi$ where $\frac bc = \tan\phi$ Given only $theta$ ...
3
votes
1answer
134 views

Proof that only a certain amount of points can fit in a rectangle

Prove that no more than 8 points can fit in a rectangle with sides d and 2d if any 2 points have to be at least d units away from each other. I have proved that no more than 6 points can fit ...
0
votes
1answer
47 views

rectangular paddock, dimensions, maximise area it encloses

Having trouble trying to work out a question which involves finding a function to graph evidence of the correct answer, any advice would be greatly appreciated. I am struggling with part 'b' a lot, ...
1
vote
2answers
30 views

Geometrical calculation to enlarge the height of rotated rectangle

There is a polygon (rotated rectangle) that defined by 4 corner points in 2D coordinate system. Does anyone help me with the fast (minimum trigonometry operations) algorithm to change its height by ...
0
votes
3answers
99 views

Find width and length of rectangle given diagonal and area

The diagonal of rectangle is 25, its area is 168, find width and length. I tried solving this problem using trigonometry since diagonal and two sides forms a right triangle, from area i got that ...
3
votes
1answer
193 views

Area of the shaded part in rectangle

The question asks you to determine the shaded part of the rectangle in terms of x. please will someone help with this problem, i have spent a while on it with not much progress.
1
vote
1answer
209 views

Area of overlapping squares

I'm working on a programming project and got to the point where I need to find how much is the blue square overlapping each of the other 9 squares. The squares' sides(including the blue one's) are ...
1
vote
1answer
64 views

Similar quadrilaterals in rectangle

While working on a problem on finding the shaded region in a rectangle, I realized that if a line cuts a rectangle into two quadrilaterals, then these two quadrilaterals are similar as the opposite ...