Problem Solving

[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

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

=>

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



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