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## Official Guide Explanation:Problem Solving #135

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: 135
Page: 79
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >

Explanation: Given that MPQT is a square, we know that all the sides of MPQT are equal. Call each side s. One of those sides is the width of rectangle MPRS, which was an area of 540. The width is s, and the length is s + 12, since PQ = s and QR = 12. Thus, we can use the area formula:

a = lw = (s + 12)(s)

540 = s2 + 12s

s2 + 12s - 540 = 0