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12 Dec 2019, 02:59
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C
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[GMAT math practice question]
The figure shows rectangle \(ABCD\) which consists of \(7\) congruent small rectangles. The area of \(ABCD\) is \(336m^2\). What is the perimeter of \(ABCD\)?
12.12PS.png [ 10.61 KiB | Viewed 3239 times ]
A. \(72\)
B. \(74\)
C. \(76\)
D. \(78\)
E. \(80\)
The figure shows rectangle \(ABCD\) which consists of \(7\) congruent small rectangles. The area of \(ABCD\) is \(336m^2\). What is the perimeter of \(ABCD\)?
Attachment:
12.12PS.png [ 10.61 KiB | Viewed 3239 times ]
A. \(72\)
B. \(74\)
C. \(76\)
D. \(78\)
E. \(80\)
12 Dec 2019, 09:12
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for each of the 7 rectangles, let the smaller side = x , and the longer side = y
it can be easily noticed from the diagram that \(3y = 4x\)
The area of the rectangle = \((x+y)(3y) = 336\)
\(4x(x+\frac{4x}{3}) = 336\)
x = 6, and y = 8
so perimeter = 76
C
it can be easily noticed from the diagram that \(3y = 4x\)
The area of the rectangle = \((x+y)(3y) = 336\)
\(4x(x+\frac{4x}{3}) = 336\)
x = 6, and y = 8
so perimeter = 76
C
15 Dec 2019, 18:25
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=>
We can put unknown variables \(x\) and \(y\) in the following figure.
12.12ps(a).png [ 13.06 KiB | Viewed 3038 times ]
We have \(4x = 3y\) or \(y = (\frac{4}{3})x\) and \(7xy = 336\) or \(xy = 48.\)
Substituting \(y = (\frac{4}{3})x\) into \(xy = 48\) gives us \(x(\frac{4}{3})x = 48, \frac{4x^2}{3} = 48, x^2 = 36,\) and \(x = 6.\)
Then \(xy = 48\) becomes \(6y = 48\) and \(y = 8.\)
We have \(x = 6\) and \(y = 8.\)
So, the perimeter is \(2(x + y + 4x) = 10x + 2y = 10*6 + 2*8 = 60 + 16 = 76.\)
Therefore, C is the answer.
Answer: C
We can put unknown variables \(x\) and \(y\) in the following figure.
Attachment:
12.12ps(a).png [ 13.06 KiB | Viewed 3038 times ]
We have \(4x = 3y\) or \(y = (\frac{4}{3})x\) and \(7xy = 336\) or \(xy = 48.\)
Substituting \(y = (\frac{4}{3})x\) into \(xy = 48\) gives us \(x(\frac{4}{3})x = 48, \frac{4x^2}{3} = 48, x^2 = 36,\) and \(x = 6.\)
Then \(xy = 48\) becomes \(6y = 48\) and \(y = 8.\)
We have \(x = 6\) and \(y = 8.\)
So, the perimeter is \(2(x + y + 4x) = 10x + 2y = 10*6 + 2*8 = 60 + 16 = 76.\)
Therefore, C is the answer.
Answer: C
