Official Guide Explanation:
Problem Solving #147




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Solution and Metadata

Question: 147
Page: 173
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Triangles > Pythag
Category 2: Geometry > Triangles > Multiple figures
Category 3: Word Problems > Geometry Problems >

Explanation: If you call the point where the right angle is located point Q, then triangle VQR is a right triangle of which two of the sides are known. We know that side VQ is 5 and the hypotenuse, VR, is 10. Thus, we can solve for the distance QR. If we call QR x, then 52 + x2 = 102 , or 25 + x2 = 100, or x2 = 75, or x = 5 rt[3]. Since RS (that's what we're looking for, after all!) is the difference between QS and QR, we can solve for it by subtraction: 10 - 5 rt[3], choice (A).

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