Bunuel wrote:
The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?
(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.
Kudos for a correct solution.Attachment:
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Solution:
We are given a rectangular rug with a uniform border. Let’s begin by sketching and labeling the dimensions of the rug and the rug’s border below.
We must determine the area of the rug that excludes the border. Thus, according to our diagram above, we must determine the product of W and L.
Note that the entire length of the rug is (L + 2x) and the entire width of the rug is (W + 2x).
Statement One Alone:The perimeter of the rug is 44 feet.
We will use the formula for the perimeter of a rectangle, which is P = 2W + 2L. Using the information in statement one, we can now create the following equation for the perimeter of the rug:
2(W + 2x) + 2(L + 2x) = 44
2W + 4x + 2L + 4x = 44
2W + 2L + 8x = 44
We see that we do not have enough information to determine the value of WL. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:The width of the border on all sides is 1 foot.
We know x = 1, but we still don’t know the value of either W or L. Thus, the information in statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:Using the information in statements one and two we know that 2W + 2L + 8x = 44 and that x = 1. So,
2W + 2L + 8(1) = 44
2W + 2L = 36
W + L = 18
Since there are many pairs of numbers that add up to 18, we can’t determine the exact values of W and L. Thus, we still do not have enough information to determine the value of WL.
Answer: E
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