Questions about rectangles and its properties.

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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 ...
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1answer
24 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 ...
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1answer
34 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 ...
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2answers
40 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. ...
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1answer
40 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 $theta$ ...
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1answer
50 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 ...
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1answer
11 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, ...
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2answers
26 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 ...
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3answers
35 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 ...
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1answer
79 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.
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1answer
72 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 ...
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1answer
33 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 ...
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1answer
83 views

Compute ratio of a rectangle seen from an unknown perspective

TL;DR: Given 4 points on a two dimentional plane, representing a reclangle seen from an unknown perspective, can we deduce the width / height ratio of the rectangle ? Details: From a picture, and ...
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2answers
113 views

How to solve this riddle?

How to solve this riddle? All rooms have the same shape and size. Every room has one entrance, and two exits: one on the left, and one on the right (on opposite directions). Both exits lead to a ...
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0answers
76 views

Calculating the Area of a Circle Occupied by a Rectangle

This is a question regarding how to calculate the area of a circle occupied by a rectangle when that rectangle is larger than the circle (see this link for a example image ...
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1answer
113 views

Area of Circle Overlapped by Rectangle

I'm trying to determine 'how much' (as a percentage) a 2D rectangle fills a 2D circle. Actual Application: I was comparing the accuracy of some computer game weapons by calculating the max possible ...
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5answers
633 views

Does rotation of a rectangle keep it rectangular?

If I rotate a rectangle by 45°, does it stay rectangular or become something else? I mean do 90° angles stay 90°? I am asking this question because I have some results where the rotated rectangle ...
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2answers
24 views

2D geometric relation in a rectangle

I'm trying to implement the Sakoe & Chiba's global constraint for the Dynamic Time Warping algorithm but I'm stuck with a geometrical problem : I'm trying to find the value of d given a, b and c. ...
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4answers
592 views

Check if a point is inside a rectangle (not knowing the coordinates, but knowing distances to vertices)

I have to solve the following problem: I have 4 points (A, B, C, D) which form a rectangle, but I do not know their coordinates. I have another point (X), I do not know its coordinates either, but I ...
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3answers
77 views

Prove this is a rectangle

Suppose we have quadrilateral $ABCD$ where $m\angle A = m\angle B = 90^\circ$ and $AB \cong CD$. Is this figure always a rectangle? If not, can someone give a counterexample? I tried drawing the ...
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0answers
24 views

Highest area rectangle in a rectangle trapezoid

There is a rectangle trapezoid with base sizes 8 and 24 and height of 12. Is there a way of finding highest area rectangle inside a trapezoid which 2 points would be in sides of a trapezoid? I ...
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1answer
30 views

Resizing Rectangular Boxes With Mouse

I'm creating a system that allows users to create objects on the screen (as rectangles) and move them around and resize them using the corners and the mouse. My only problem is, when one of the ...
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2answers
38 views

How to detect all points of rectangle by given one point A, height, width, and angle between AC and X axis? [closed]

How to detect points B, C, D of rectangle with given point A, height, width and angle L between AC and X axis.
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3answers
179 views

How to check if two rectangles intersect? Rectangles can be rotated

How to check if two rectangles intersect? Each rectangle is defined by three points in 2d space. The rectangles can be rotated around any point as on the image below.
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0answers
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Finding optimal height for objects in 2D packing

I have a problem that I need to find the right algorithm for and I am not sure which avenues are going to be easiest. I have a 'row' of fixed height and we can assume infinite length. fig.1 ...
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1answer
75 views

In Neutral Geometry, prove that the opposite sides of a rectangle are congruent.

I'm having some trouble proving a theorem of Neutral Geometry. First, allow me to clearly state what we are allowed to assume in Neutral Geometry: Hilbert's incidence axioms Hilbert's order axioms ...
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Does a point quadrilateral form a rect in 3D space?

I have 4 points with x and y coordinate and would like to find out a way to check if given quadrilateral would be a rectangle in 3D space. I tried a bunch of conditions, but there was always and edge ...
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27 views

Maximize the intersection over union of oriented rectangles

I have an oriented rectangle in the form region=(x1,y1, ..., x4, y4) I want to know which is the axis-aligned rectangle with the same center that maximize the intersection over union of the areas of ...
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1answer
67 views

Find maximum width of a rectangle contained with another (diagonally)

It appears that the question of figuring out if a rectangle will fit inside of another, specifically at a diagonal, has been asked before. As such, utilizing the equation linked here, I was able to ...
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1answer
153 views

Dimensions of a paddock (3 sides of a rectangle) to enclose maximum possible area

I need help with Qs 4, 5 and 6!! Three sides of a rectangular paddock are to be fenced, the fourth side being an existing straight water drain. If 1000m of fencing is available, what dimensions ...
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1answer
64 views

How to find one side of a rectangle, if I have other side and slope

So suppose I have the width of a rectangle that is 1000 cms and its slope that is at 20 degrees. How can I calculate the other length required for the height of this rectangle....
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2answers
65 views

Finding the greatest possible dimension of a rectangle

Here's the question: If the greatest possible distance between two points within a certain rectangular solid is 12, then which of the following could be the dimension of the solid? A) 3x3x9 B) 3x6x7 ...
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trigonometry - find coordinates of inner triangle after rotation

here is my situation: I have a rectangle I'm rotating 30 degrees counterclockwise, how could I use trig to get the 3 vertices (corners) and lengths of the purple triangle sides and hypotenuse ...
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3answers
292 views

Finding the area of the 4th triangle, given the areas of the other 3, and all the 4 form a rectangle

In one of my tutorial classes, when I was studdying in 9th class (I am in 10th now), our tutor gave us a problem saying it’s a difficult one, and to him, it was incomplete. This is that problem: ...
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1answer
24 views

find the distance of a point from the sides of a rectangle

I would like to find the distance of a point from the sides of a rectangle. here is various examples: t(x,y) is a point within the rectangle (WxH). We have two angles (1-3 angle is 90 and for Fig ...
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4answers
104 views

Maximum area of a rectangle

Two concentric circles have radii 13 and 15. Let ABCD be a rectangle, so that A and B lie on the larger circle, and C and D lie on the smaller circle. Find the maximum area of rectangle ABCD. I tried ...
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1answer
34 views

Work Out Height Based on Width and Ratio

I'm trying to work out the height of an image. I have this data available to me: width: 320 ratio: 0.66 Is it possible to work out the height based off the data ...
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1answer
140 views

Find the area of the shaded region

This is the Figure, $ABCD$ is a square , $AB = BC = CD = DE = 21cm$. $AC$ and $BD$ are the diagonals of the square. The two semi circles are drawn with $AD$ and $BC$ as diameter. Find total are of ...
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1answer
28 views

Find longer side of a rectangle with respect to another rectangle

So I have two rectangles: Rectangle R1 with width r1w and height r1h Rectangle R2 with width r2w and height r2h I can find the slope/aspect ratio of the two ...
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1answer
36 views

How to find the side for the biggest area?

Let $x$ be one side of a rectangle and $a$ its perimeter. We know that it's area is given by: $$ S = x\cdot\left(\frac{a}{2}-x\right). $$ $$ S=-x^2+ax/2$$ where a=-1, b= a/2 and c= 0 $$D=a^2/4$$ ...
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3answers
106 views

Squaring of the circle

From curiosity I read about enhancements of the squaring of the circle. Right now I do not see what is wrong with the following approach: Archimedes devised that the surface of a circle equals the ...
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1answer
179 views

Geometry: Construct a rectangle with area equal to a given triangle and with one side equal to a given segment.

So we have triangle, ABC, and line segment DE. We don't know anything about them other than ABC is a triangle of some sort and DE is a line segment. We're tasked with constructing a rectangle such ...
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0answers
54 views

Dividing rotated rectangle into equal area grid

I have a rotated rectangle that is represented by the coordinates of its 4 vertices (Actually represented by 4 lat-lon). I want to divide the rectangle into equal area grids. I need this to find the ...
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0answers
117 views

Geometry question: translating a rectangle according to a specific rule

Please take a look at the figure below. I have two line segments: a, which goes from point A to point B, and b, which goes from point B to point C. Each line defines a rectangle, which has width d and ...
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1answer
91 views

Largest rectangle bounded under a function

Let $f$ be a positive monotonically increasing real function in $[0,1]$. Let $F$ be the area under the curve of $f$ ($F=\int_0^1{f(x)dx}$) For every $x\in[0,1]$, let $G(x)=f(x)*(1-x)$ = the area of a ...
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2answers
165 views

How many unit squares can overlap a given unit square without overlapping each other?

How many unit squares can overlap a given unit square without overlapping each other? @calculus has managed to arrange 7 squares (see this GeogebraTube page). This seems like the maximum ...
16
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1answer
239 views

Under what conditions will the rectangle of the Japanese theorem be a square?

In geometry, the Japanese theorem for cyclic quadrilaterals states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Question. Under ...
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1answer
194 views

Geometrical calculation to determine size difference between two rectangles when rotating one

I've asked a programming question on StackOverflow here which should give you a good understanding why I'm trying to do this. I'm asking it here because it's now down entirely to the mathematics of ...
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1answer
332 views

Find other coordinates on a rectangle given 1 side length and 2 opposite points

I have two problems I'm hoping to solve with one equation for a game. This game uses a square for its key (rotates) but I'd prefer to treat it as a rectangle instead. I want to find the coordinates so ...
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1answer
28 views

Point in a rectangle

$ABCD$ is a rectangle and $P$ is a point in the same plane. If the perpendicular through $C$ to $AP$ and the perpendicular through $B$ to $DP$ intersect at $Q$, prove that $PQ \parallel AD$. ...