# Questions tagged [rectangles]

Questions about rectangles and their properties.

590 questions
Filter by
Sorted by
Tagged with
1 vote
137 views

### 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 $a$ = ...
58 views

### 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 ...
55 views

### 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 $\angle (BAO-OBC)$?
1 vote
232 views

### 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 $T$...
274 views

### 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 ...
1 vote
72 views

### 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 $xy=3x+3y+\sqrt{9x^2+9y^2}$, ...
1 vote
77 views

### 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 ...
1 vote
68 views

### 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 ...
105 views

### 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 $AC^2 = 4*ME*MF$ ...
114 views

### 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 ...
30 views

### 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 ...
162 views

126 views

### 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 ... 104 views

### 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 ...
35 views

### 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 ...
45 views

### 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 ...
99 views

### 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. ...
57 views

1 vote