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Bunuel

The above figure represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 18


Attachment:
2017-11-07_0941.png


Let a and b represent the sides of the rectangular garden. Since the walk is 3 feet wide on two opposite sides and 2 feet wide on the other sides, the sides of the square are a + 6 and b + 4. Since the sides of a square are equal:

a + 6 = b + 4

b = a + 2

Thus, the area of the rectangular garden is ab = a(a + 2) = 48. Let’s solve this for a:

a(a + 2) = 48

a^2 + 2a - 48 = 0

(a - 6)(a + 8) = 0

a = 6 or a = -8

Since the side of a rectangle cannot be negative, we must have a = 6. Thus, the side of the square plot is x = a + 6 = 12.

Answer: C
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