Official Guide Explanation:
Problem Solving #76




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Solution and Metadata

Question: 76
Page: 71
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Algebra > Simplifying Algebraic Expressions >

Explanation: Call each side of a square s. If the area is n:

s2 = n

s= rt[n]

We're looking for the length of the diagonal. That's the hypotenuse of a right triangle formed by two sides and the diagonal; the two sides are the legs of the triangle. Because this is a square, the triangle is a 45:45:90 triangle, meaning that the hypotenuse (the diagonal) is rt[2] times the length of either leg. Since the legs are rt[n], the diagonal is:

rt[n] rt[2]= rt[2n], choice (A).

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