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## Official Guide Explanation:Problem Solving #102

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: 102
Page: 166
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Special Tris

Explanation: The diagonal of a square is the hypotenuse of an isoceles right triangle formed by two of the sides and the diagonal. The angles in the right triangle are 45:45:90, which means that the sides are related by a ratio of x:x:x rt[2]. Since the hypotenuse (the diagonal of the square) is 20, x rt[2] = 20, or x = (20/( rt[2])). We're looking for the perimeter, or four times the length of one side: 4x = 4((20/( rt[2]))) = (80/( rt[2])) ≈ (80/(1.4)) = 60, choice (B).

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