Math: 58dcc59f

ID: 58dcc59f

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Remember factor trees?

Method 1: An understanding of number properties can help considerably with these algebra questions that would force you to conjure up the correct binomials, multiply, and then solve. Consider the prime factorization of 104: 52 * 2 --> 26 * 2 * 2 --> 13 * 2 * 2 * 2. That is it. Those prime factors can be combined in different ways to produce unique factors of 104, but here, the problem tells us that the length (of the fence) is 5 feet longer than the width. The only factors that will be 5 apart are 13, which cannot be further reduced, and 8 (from 2 * 2 * 2), so we can answer the question directly. As the length is the lengthier dimension, the correct answer must be 13.

Method 2: You can put Desmos to use by mapping the length onto, say, y, and the width onto x.

The graphs intersect at the point (8, 13), where the lengthier "side" is 13. Thus, the correct answer is 13.

Method 3: By far the worst way to solve the question is to work out the algebra by hand, but provided you are decent at algebra, you should still arrive at the solution within 1-2 minutes.

L = W + 5

LW = 104 --> W(W + 5) = 104

W^2 + 5W - 104 = 0

(W + 13)(W - 8) = 0

W = -13 or 8

Since the width of a fence cannot be negative, the only valid solution is 8; if the fence is 8 feet in width, then it must be 8 + 5 feet in length, and the correct answer is 13.