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by bacali » Fri Nov 14, 2008 12:03 pm
Two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18root2, then what is the perimeter of each square? (in the image the two squares have one vertex to against one end of the rectangle and the other touching the vertex of the other square. they're both tilted...)


A. 8root2
B. 12
C. 12root2
D. 16
E. 18
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by dmateer25 » Fri Nov 14, 2008 12:25 pm
The length of the rectangle is the 2 diagonals from the squares.

The width of the rectangle is 1 diagonal.

So 6 diagonals would equal the perimeter of the rectangle. We know the perimeter is 18root2.

18root2 / 6 = 3root2

each diagonal is 3root 2 and that means that each side of the squares is equal to 3. (because the diagonal of a square is length of side*root2)

Perimeter of square would equal 3 x 4 = 12

B
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by bacali » Fri Nov 14, 2008 12:32 pm
Great explanation. I was making it much more complicated than it was.

Thanks.
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by srisl11 » Fri Nov 14, 2008 12:44 pm
Let assume that side of the square = x

then Perimeter of square 1 + perimeter of square 2 - the sides of the square inside the rectangle = perimeter of rectangle

So 4x+ 4x - 2x = 18 root(2)
6x= 18 root (2)
x = 3 root (2)

Perimeter of square = 4x = 12 root (2)
ans C
Correct me if I'm wrong
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by srisl11 » Fri Nov 14, 2008 12:56 pm
or from the diagram you can just say

6x = perimeter of the rectangle
6x = 18 root (2)

perimeter of square = 4x = 12 root (2)
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by dmateer25 » Fri Nov 14, 2008 1:01 pm
The image would look like this:

ImageImage[/img]
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by srisl11 » Fri Nov 14, 2008 1:28 pm
GOT IT ...THANKS!!
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