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Updated on: 08 Jan 2021, 02:45
Originally posted by udaymathapati on 27 Aug 2010, 23:01.
Last edited by Bunuel on 08 Jan 2021, 02:45, edited 2 times in total.
Last edited by Bunuel on 08 Jan 2021, 02:45, edited 2 times in total.
Edited the question.
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In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18√2, then what is the perimeter of each square?
A. 8√2
B. 12
C. 12√2
D. 16
E. 18
Attachment:
Rectangle.png [ 19.46 KiB | Viewed 66554 times ]
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28 Aug 2010, 07:45
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In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18√2, then what is the perimeter of each square?
A. 8√2
B. 12
C. 12√2
D. 16
E. 18
The rectangle's \(width=d\) and \(length=2d\), where \(d\) is the diagonal of each square.
\(P_{rectangle}=2(d+2d)=18\sqrt{2}\);
--> \(d=3\sqrt{2}\).
Now, \(d^2=s^2+s^2\), where \(s\) is the side of a square:
--> \(d^2=(3\sqrt{2})^2=18=2s^2\)
--> \(s=3\)
--> \(P_{square}=4s=12\).
Answer: B.
28 Aug 2010, 07:45
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Hello 
Let's name:
A width of the rectangle (the biggest line)
B height of the rectangle (the smallest line)
C width of the square
We know that 2 (A + B) = 18√2, so A + B = 9√2
We can also infer that A = 2B since A = 2 diagonal of the square and B = 1 diagonal of the square (see it on the figure to understand it more easily)
A = 3√2 and B = 6√2
From Pythagor, we have C² + C² = B²
<=> 2c² = (3√2)²
<=> 2c² = 9 * 2
<=> C = 3
So the perimeter of each square is 4 * 3 = 12
Let's name:
A width of the rectangle (the biggest line)
B height of the rectangle (the smallest line)
C width of the square
We know that 2 (A + B) = 18√2, so A + B = 9√2
We can also infer that A = 2B since A = 2 diagonal of the square and B = 1 diagonal of the square (see it on the figure to understand it more easily)
A = 3√2 and B = 6√2
From Pythagor, we have C² + C² = B²
<=> 2c² = (3√2)²
<=> 2c² = 9 * 2
<=> C = 3
So the perimeter of each square is 4 * 3 = 12
