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## Official Guide Explanation:Problem Solving #24

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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