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Geometry

Problem Solving — algebra and arithmetic
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by VenugopalGurram » Thu Dec 06, 2012 12:04 am
In the figure Shown,two identical squares are inscibed in the rectangle.if the area of the rectangle is 36 Sq. Units,then what is the perimeter of each Square??
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sorry for the figure...
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by David Mahler » Thu Dec 06, 2012 7:16 am
Notice first that the long side of the rectangle (width) must be twice as long as the short side (height). Label the height x and the width 2x.

The area of the rectangle is then 2x^2, which equals 36:

2x^2 = 36
x^2 = 18
x = 3root(2)

If the height is 3root(2), then the diagonal of each square is 3root(2). Not that the diagonal of a square is also the hypotenuse of a 45-45-90 triangle. The ratio of sides in a 45-45-90 triangle is x : x : xroot(2). If the hypotenuse is 3root(2), then the length of each side is of the square is 3.

Therefore, the perimeter of each square is 4 * 3 = 12.
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by sana.noor » Mon Jun 24, 2013 11:15 pm
just looking at the figure how can you say that long side is twice the short side. the figure is not always drawn to scale. it could be any value
1) 2 into 18
2) 3 into 12
3) 4 into 9

i must say that the real question is missing something.
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by jitsy » Sat Jul 20, 2013 1:46 pm
sana.noor wrote:just looking at the figure how can you say that long side is twice the short side. the figure is not always drawn to scale. it could be any value
1) 2 into 18
2) 3 into 12
3) 4 into 9

i must say that the real question is missing something.
If the question does not say that the figure is not drawn to scale, we assume its more or less what it looks like. If nothing else if given, I'd just assume the sides of the rectangle as 4*9. Then obviously just calculate the side of the square using the pythagoras formula (or even the isosceles triangle rule) and arrive at the answer.
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by Jim@StratusPrep » Mon Jul 22, 2013 10:13 am
The solutions above are great. Remember that when you are going through geometry problems that you only have to know a few certain things. The GMAT will test you be putting information in different formats (i.e. rotating the square) but you still only have a few ways that you can use the figures.
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by kumudkantish » Wed Jul 24, 2013 4:08 am
2 identical square inside rectangle.
We can make 4 identical square out of all the area of this rectangle.
So, 36= 4 . side square ( area of square= side square )
Side of each square , 9 = side square
Side= 3
Now, perimeter of two distinct square inside the rectangle is 3 . 4 = 12.

Hope this approach is correct for quick response.
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