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The figure shows rectangle ABCD which consists of 7 congruen

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by Max@Math Revolution » Thu Dec 12, 2019 1:32 am
[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?

A. 72
B. 74
C. 76
D. 78
E. 80

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by henilshaht » Thu Dec 12, 2019 9:53 am
Let's call the length of the bigger rectangle L,
the width of the bigger rectangle W

And the length of one of the smaller rectangle l,
the width of one of the smaller rectangle w.

AD = BC => w + w + w = l + l + l + l => 3w = 4l => w = 4l/3

Similarly AB = CD = l + w = l + 4l/3 => 7l/3

Area of the bigger rectangle is 72
LW = 72 => (7l/3)(4l) = 72 => l = 6
and w = 8

So, L = 6 + 8 = 14,
W = 4(6) = 24

Perimeter = 2L + 2W = 2(14) + 2(24) = 76
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by Max@Math Revolution » Sun Dec 15, 2019 5:01 pm
=>

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

Image

We have 4x = 3y or y = (4/3)x and 7xy = 336 or xy = 48.
Substituting y = (4/3)x into xy = 48 gives us x(4/3)x = 48, 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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