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## Official Guide Explanation:Problem Solving #152

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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: 152
Page: 174
Difficulty: 5 (Moderate)
Category 1: Geometry > Triangles > other
Category 2: Geometry > Triangles > Multiple figures
Category 3: Word Problems > Geometry Problems >

Explanation: The area of a triangle is (1/2)bh, so in this case, (1/2)xy = 24. Since x = y + 2, we can substitute that into the area equation:

(1/2)(y + 2)(y) = 24

y2 + 2y = 48

y2 + 2y - 48 = 0

(y - 6)(y + 8) = 0

y = 6, y= - 8

Since the side of a triangle cannot be negative, y = 6. If y = 6, x = 8, and using the 3:4:5 ratio for right triangles, we know that the hypotenuse, z, is 10, choice (E).

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