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The figure shows rectangle ABCD which consists of 7 congruent small re

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The figure shows rectangle ABCD which consists of 7 congruent small re  [#permalink]

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New post 12 Dec 2019, 01:59
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Question Stats:

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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 \(ABCD\)?

Attachment:
12.12PS.png
12.12PS.png [ 10.61 KiB | Viewed 528 times ]


A. \(72\)

B. \(74\)

C. \(76\)

D. \(78\)

E. \(80\)

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Re: The figure shows rectangle ABCD which consists of 7 congruent small re  [#permalink]

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New post 12 Dec 2019, 08:12
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
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Re: The figure shows rectangle ABCD which consists of 7 congruent small re  [#permalink]

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New post 15 Dec 2019, 17:25
=>

We can put unknown variables \(x\) and \(y\) in the following figure.

Attachment:
12.12ps(a).png
12.12ps(a).png [ 13.06 KiB | Viewed 376 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
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Re: The figure shows rectangle ABCD which consists of 7 congruent small re  [#permalink]

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New post 09 Jan 2020, 04:57
MathRevolution wrote:
[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 \(ABCD\)?

Attachment:
12.12PS.png


A. \(72\)

B. \(74\)

C. \(76\)

D. \(78\)

E. \(80\)


Pretty Innovative Question and the moment you see the first step of Official Solution you can solve on your own :-D :-D :-D

Bump up!
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Re: The figure shows rectangle ABCD which consists of 7 congruent small re   [#permalink] 09 Jan 2020, 04:57
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