# Questions tagged [rectangles]

Questions about rectangles and their properties.

400 questions
1answer
28 views

### Is packing rectangles exactly into a larger rectangle NP-complete?

I want to pack a number of rectangles into a larger rectangle, however, unlike other questions that I could find, I would like to do so exactly, without allowing any wastage. I do not really care ...
3answers
66 views

### If a rectangle can be split into n and into n+14 squares, then n=18. What is the meaning of this

This problem seems to be a geometrical one, but actually it is an algebraic one. If you split the rectangle into n squares and into n+k squares, then what does that means? What is this supposed to ...
1answer
77 views

### Shortest distance between two rectangles in 2D

Given the center points and dimensions of two rectangles and the angles $\theta_1$ and $\theta_2$, how to calculate the shortest distance between two rectangles ($d$)? $\theta$ is the angle that the ...
0answers
8 views

### Collision resolution of rotated rectangles

Imagine two rotated rectangles that overlap/intersect in R². How far in each axis would rectangle A (in red) have to be translated to no longer intersect rectangle B (in blue) given the center of ...
1answer
31 views

### Maximizing the size of n similar equilateral triangles from a rectangle

I have 3 rectangles of greenhouse sheeting material. They are each 12 feet long and 4 feet high. I want to use this material to clad a 3/4 icosahedron dome structure. What that means is that I will ...
0answers
21 views

### Find a point on a circle which contains a rectangle using another point, the angle between the two and the rectangle's dimensions

I'm trying to construct a mathematical formula that will calculate a point (x,y) on a circle which contains a rectangle with a width ...
0answers
27 views

### How to fill a rectangle with smaller specific rectangles that have cardinal information about their adjacent neighbours

Lets say its 6x6 grid that is represented by top left(0,0) and bottom right(1,1) in coordinate system. Next, I have set of objects with their cardinal directional information about each of their ...
1answer
50 views

### How to find sides of rectangle that is inscribed in other rectangle?

We have smaller rectangle inscribed in the bigger rectangle as shown on the picture. The bigger outer rectangle is inclined for a certain angle. We know height and width of the bigger rectangle and ...
0answers
19 views

### Scaling rectangle and keeping ratio when height and/or width exceed container

I have a 2D box with a Height of 206 and a Width of 202. Inside of this box is a Rectangle. ...
1answer
23 views

### Calculate resizing factor for N small rectangles inside a large rectangle to cover maximum area

I have a variable number of small rectangles which are natively 39 x 83 (width by length). I will also have an arbitrary sized, container rectangle that I need to fit all of the smaller rectangles ...
1answer
34 views

### Ratio between the areas of two rectangles inscribed in a triangle and the area of the triangle

Let's denote $A(X)$ the area of the polygon $X$. Let $S$,$R$ be rectangles inside a triangle $T$. Find the maximum value of: $$\frac{A(R)+A(S)}{A(T)}$$ My try The only property i know (from a ...
1answer
41 views

### Edges of rectangle mapped to a new plane

If a rectangular plane lies in quadrant I and is transformed by a polynomial function, will the edges of the rectangle always map to the edges of the transformed plane? Will all points along the ...
0answers
29 views

1answer
39 views

### What is the area of the rectangle?

The diagram shows a rectangle and a line X parallel to its base. Two points A and B lie on X (A is outside and B is inside the rectangle). The sum of the areas of the two shaded triangles is 10cm. ...
1answer
31 views

### How to re-scale a rectangle to a smaller area?

I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about ...
1answer
47 views

### What is the value of $a+2b$ if $\frac{OP}{EF}=\frac{a}{}b$ in $ABCD$ rectangle?

BD is diagonal in ABCD rectangle and E, F is the mid point of BC, CD respectively. Line BD intersects AE, AF at O, P respectively. If $\dfrac{OP}{EF} = \dfrac{a}b$, then a+2b=?
1answer
99 views

### Tiling a 7x9 rectangle with 2x2 squares and L-shaped trominos

It's possible to cover a 7x9 rectangle using 0 2x2 squares and 21 L-shaped trominos, for example: ...
1answer
102 views

### Arrange $n$ tiles in a rectangle pattern

Is there a way to find how to arrange $n$ tiles in order to form a rectangle that is closest to a square? As I result I am looking for the dimension of that rectangle if it exists. For example, here ...
1answer
43 views

### Maximized dimensions of bounding box around rotated rectangle [closed]

Given an orthogonal rectangle with sides a and b, what rotations $\theta$ result in a bounding box with maximum height c.q. ...
0answers
18 views

0answers
12 views

### Adjust overlaying square (x, y) when parent square's anchor is changed.

I'm working on a project that involves drawing shapes on a grid using a WebGL rendering library. Currently, I have to draw a simple rectangle and then draw another rectangle on top of that rectangle, ...
2answers
39 views

### center of gravity given four weights [closed]

I have this problem. I have four points that corresponds to four vertices of rectangle. Every vertex has a load cell that return a weight. How can I calculate the center of gravity, in a range of 0-...
2answers
208 views

### Is it always possible to cut disjoint 0.359 of two rectangles?

There are two rectangles, red and blue. Is it always possible to cut two disjoint rectangles, one containing 0.359 the area of red and one containing 0.359 the area of blue? The following figure ...