Official Guide Explanation:
Problem Solving #24




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Solution and Metadata

Question: 24
Page: 65
Difficulty: 5 (Moderate)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Quadrilaterals >
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: The problem gives you two equations. First, the perimeter is 34 = 2l + 2w. Second, the area is 60 = lw. To combine the equations, set the second equal to w, then substitute into the first equation: w = (60/(l)), then

34 = 2l + 2((60/(l)))

17 = l + (60/(l)) (divide each term by two)

17l = l2 + 60 (multiply each term by l)

l2-17l + 60 = 0

(l - 12)(l - 5) = 0

l = 12 or l = 5. Thus, the longer side is 12, choice (D).

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