Official Guide Explanation:
Problem Solving #102




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Solution and Metadata

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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