Questions about rectangles and its properties.

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1answer
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Size of minimal covering, overlapping and disjoint

There are two ways to cover a geometric shape with primitive units: you can allow the units to overlap, or require that they be disjoint. Of course the number of units in the case of disjoint covering ...
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0answers
17 views

Find bounding box dimensions around rotated object

Consider the following rectangle with dimensions 320 by 130. After rotating the rectangle 10 degrees clockwise from the center (x: 160, y: 65), it looks like this. My question is: How do ...
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3answers
36 views

Inscribe a rectangle inside an ellipse

A rectangle is to be inscribed inside a horizontal ellipse (whose major or minor axis is parallel to x axis). Is the horizontal orientation of the rectangle (two sides parallel to x axis) the only ...
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2answers
41 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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2answers
34 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
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1answer
19 views

Divide-and-conquer on a rectilinear polygon

A rectilinear polygon can be characterized by its cover number - the smallest number $k$ such that the polygon can be covered by $k$ possibly overlapping squares. For example: For a square, $k=1$. ...
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3answers
21 views

Volume of a rectangular prism's walls

Sorry if this is an obvious question... I have been trying to figure this out for a little while and come up with nothing... If I have a rectangular prism, say $5\times10\times12$ meters, it has a ...
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10answers
3k views

Why is a rectangle a parallelogram, but a parallelogram is not a rectangle?

It confused me that a parallelogram is never considered a rectangle, yet a rectangle is considered a special case of a parallelogram. How is this possible?
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1answer
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I know the perimeter of the rectangle but not the area. How do I find the length and width? [on hold]

The perimeter of the rectangle is 986. I don't know the area and I need to find the length and width. The problem states that the length is 199 ft more than the width. That is all the information that ...
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2answers
27 views

Percentage size of the rectangle over the inner rectangle

I need to know how much I need to zoom (in percent) the inner box to rotate the outer rectangle 12 degrees and he touched the inner rectangle with four sides on the perimeter. For example, I have ...
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2answers
78 views

Can a polygon have four 90 degree corners and still not be a rectangle?

On another woodworking forum, someone said that after building a case, you should measure the diagonals to ensure the case is square and that just checking if all the corners are 90 degrees won't ...
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2answers
40 views

Find the dimensions of the rectangle having the largest area

A rectangle is bounded by the positive $x$-axis, positive $y$-axis and the line with equation $3y= 16-2x$. Find the dimensions of the rectangle having the largest area. \begin{align} & y= ...
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3answers
167 views

Smallest square containing a given triangle

Given a triangle $T$, how can I calculate the smallest square that contains $T$? Using GeoGebra, I implemented a heuristic that seems to work well in practice. The problem is, I have no proof that it ...
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0answers
43 views

Simple notation questions(2) and unit tangent vector question(1)

I have a vector field $F$, and a rectangle $C$ and some $T$ as a unit tangent vector to $C$ directed anticlockwise around $C$. How is $T$ calculated? Wouldn't it just be a straight line facing ...
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1answer
27 views

Finding the side lengths of a rectangle given a circle passing through one of its vertices and touching two of its sides

A circle touches a rectangle $ABCD$ of side lengths $2a$ and $2b$ at $M$ and $N$ on sides $AB$ and $AD$ respectively. It also passes through the point $C$. If the perpendicular distance of the line ...
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1answer
28 views

Find f with A plane curve whose equation is $y - f (x) = 0$ passes through the origin.

A plane curve whose equation is $y - f (x) = 0$ passes through the origin.Consider the rectangle $R_x$ formed by the coordinate axes and lines parallel to the axis passing through the point $(x, f ...
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1answer
37 views

Crazy rectangles, semi-circles, and circles!

Problem is to find the ratio of the area of the circle to that of the semi-circle. Note that points $F$ and $E$ weren't given in the original diagram, and that the circle at the top-right ...
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1answer
37 views

What is the greek symbol that represents the ratio of the length and with in a rectangle.

I understand that there is pi, but I was provoked by a question that asked this, "I have a rectangle and if I cut a square off of it it produces the same type of rectangle. I know that the width is 1 ...
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1answer
14 views

Proving that a relation is acyclic

Let $S$ be the set of triples of positive numbers $(x,y,s)$. Let $R$ be a directed relation defined between triples, such that $R(b,a)$ if at least one of the following four conditions hold: ...
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0answers
53 views

Staircase Lemma

Let $S$ be a staircase-shape contained in the north-eastern quarter-plane. Let $k$ be the number of its south-western corners. In the staircase shown below, there are $k=4$ corners: In each corner ...
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2answers
111 views

Optimization of the surface area of a open rectangular box to find the cost of materials

A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of the box is twice its width. Material for the base costs ten dollars per square meter and for the ...
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2answers
45 views

Geometry Right triangles in a rectangle, find the area.

Please help, I've been struggling to figure out this problem for too long... Given the area of rectangle $ABCD = 1200 \text{ unit}^2$, find the area of right triangle $ABE$
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1answer
52 views

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $ \overline{AS}$ and $\overline{AT}$

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $\overline{AS}$ and $\overline{AT}$ trisects $\angle DAB$. If $CT = 3$ and $DS = 6$, then what is the area of $ABCD$? I have ...
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2answers
725 views

Find the area of shaded triangle inside of a rectangle.

In rectangle $ABCD$, $ P$ is the mid point of $AB$. $S$ and $T$ are the points of trisection of $DC$. If area of the rectangle is $70$ square units, with reference to the figure find area of shaded ...
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1answer
199 views

Working algorithm for testing two rectangles for overlapping in Earth GPS coordinates plain

Here is a seemingly simple, but actually quite tricky problem: I am trying to figure out the correct algorithm to test intersection/overlapping of two rectangles, which are plotted on the Earth's ...
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1answer
24 views

Filling the Unit Disk With Non-overlapping Rectangles

It intuitively seems to be true that no finite set of non-overlapping rectangles can fill the unit disk. Is this proposition really true? If so, how can one prove it?
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1answer
25 views

How to determine coordinates on two different size rectangles

Hello community I hope all is well. I was wondering if someone could shine some light on the following problem. Let's say we have 2 rectangles (A and B) which are different in size. Let's say I have ...
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0answers
13 views

Making a Circle of Rotated Rectangles

By default, the system I'm using bases rectangle position by their center. If I copy a rectangle and rotate it, the result will look like this: Because I am trying to make a circle out of these ...
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1answer
81 views

How do I calculate the angle to place rectangles side by side around a circumference?

I have a circle with radius $r$ and several rectangular objects. All rectangles have the same sides $a$ and $b$ (although the side $a$ may be different from side $b$). I would like to place the ...
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1answer
35 views

Two-color square arrangement

There are $n$ green axis-parallel squares on the plane. You may scale and translate each square arbitrarily, as long as no two of them intersect. Now you have to put paiwise-disjoint red squares on ...
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1answer
58 views

Colorful squares arrangement

Can you arrange a finite number of green and red squares on the plane, sides parallel to the axes, such that: Every red square intersects $M$ green squares and no red square; Every green square ...
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1answer
116 views

9 rectangles have the same area as 20 squares

This is a fun little question that I encountered on a problem solving assessment: A small area is covered by 20 identical square tiles or 9 identical rectangular tiles. The length of the side of ...
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1answer
89 views

Least greedy square

There are $n$ squares of $m$ different colors. Squares of the same color are interior disjoint, but squares of different colors may intersect. For every square, define its "greed" as the maximum ...
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4answers
109 views

Prove that between rectangles of a given $A$ area the square is the one with lower perimeter?

Prove that between rectangles of a given $A$ area the square is the one with lower perimeter? Im lost, cant even figure out what to do, or where to start?
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0answers
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Representing a 2D function as a sum of rectangles of arbitrary shape and orientation

Suppose I am given a non-negative function $f(x,y)$ defined for $x \in [0,1]$ and $y \in [0,1]$. I'd like to represent this function as a weighted sum $w_i$ of a small number of rectangular apertures. ...
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3answers
228 views

Sum of the area of all the rectangles in a rectangular

We have a rectangular shape with the size n × m meters is divided into rectangles of size 1 × 1 meters. Question: Sum of the area of all the rectangles that can be seen in that rectangular is how ...
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2answers
216 views

Question on surface area and volume of cuboid

I came across a question: The surface area of the six faces of a rectangular solid are 4, 4, 8, 8, 18 and 18 square cms. The volume of the solid, in cubic centimetres is __. I can guess that 4 ...
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5answers
78 views

Mensuration question about a hoop resting on a staircase

I came across a question recently: A hoop, as shown in the diagram, rests vertically at stair case. Note: AB = 12 cm, and BC = 8 cm. Find the radius of the hoop. Figure (hand-made): This is ...
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4answers
108 views

Mensuration question

I recently came across a puzzling question: Two rectangles ABCD and DBEF are as shown in the figure. The area of DBEF is: Figure (hand-made): I know that through Pythagoras, we get ...
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1answer
211 views

Maximum area of a rectangle inside a triangle

I recently came across a problem where it gave a triangle with integer side lengths, and it asked you to find the maximum area of a rectangle of a triangle. I solved the problem correctly, but it ...
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2answers
110 views

Ellipse bounding rectangle

I'm trying to find the ellipse that bounds a rectangle in a way that the "distance" between the rectangle and the ellipse is the same vertically and horizontally. Here is an image to illustrate what ...
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2answers
421 views

how many rectangles in this shape

I've learned in my high school the solution to such riddle: How many rectangles are there in this shape: the solution is through combinations: in this shape is a $5\times 6$ grid so the number of ...
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2answers
54 views

Disjoint rectangles with points at their corners

There is a set of $n$ points in the 2-dimensional plane. All x values and all y values are different. We want to draw the largest set of axis-parallel rectangles such that: All rectangles are ...
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1answer
94 views

Find Cathetus C1, C2 Knowing Hipotenuse or Find C1, C2, C3, C4 of Rectangle

I have a rectangle. I know all sides and 4 points for it (see black rectangle below). I resize one edge of this rectangle to any point (see resized red color rectangle and new point B). Here is the ...
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2answers
114 views

radius of circle inscribed in rectangle

I have two circles inside a rectangle(4 * 6), where the diameter of one of both is the total length of a side of the rectangle, and the other circle diameter is part of the length of the another side. ...
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2answers
465 views

Derive formula for area of a circle from formula from area of rectangle

I need to explain how to derive the formula for the area of a circle from the formula for the area of a rectangle. The area of a rectangle is length(width) and the formula for the area of a circle is ...
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2answers
61 views

How can i figure out the points of a rectangle by just knowing the origin, width and length?

I've come across a mathematical problem, which I can't seem to solve with my limited geometry and trigonometry knowledge or by help of Wikipedia. I need to know the coordinate points of each corner ...
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0answers
26 views

Adjacency corner case

If two rectangles touch, but only touch at one of their corners (example, Rectangle A's upper-right corner is touch Rectangle B's lower-left corner), are they adjacent to one another? Why or why not?! ...
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1answer
92 views

Cutting rectangles while keeping the remainder connected

There is a cake with $n$ toppings. I want to cut a small piece out of each topping, such that the remaining cake is connected. Is this always possible? SOME FORMAL DETAILS (possibly not all of them ...
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2answers
42 views

Problem with finding “x” in triangle

I have got a problem with finding the x. I think the question isn't true or there should more informations on it.