Official Guide Explanation:
Problem Solving #177




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Solution and Metadata

Question: 177
Page: 177
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag
Category 3: Geometry > Rectangular Solids and Cylinders > Rectangular Solids

Explanation: The longest straight - line distance inside a rectangular solid is a diagonal from (for example) the lower front right corner to the upper back left corner. To find that, first find the length of a diagonal running through the base. In this case, it's the hypotenuse of a right triangle with sides 10 inches (width) and 10 inches (length). Since the sides of an isoceles right triangle are related in the ratio x:x:x rt[2], that means the diagonal running through the base has length 10 rt[2]. Now, imagine a triangle where the base is that diagonal and the height is one of the vertical sides that intersects that diagonal. The longest straight - line distance is the hypotenuse of the triangle formed by those two sides. Those sides have length 10 rt[2] and 5 (the height of the solid), so you can use the pythagorean theorem to find the hypotenuse:

(10 rt[2])2 + (5)2 = c2

200 + 25 = c2

c2 = 225

c = 15, choice (A).

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