Official Guide Explanation:
Problem Solving #113




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Solution and Metadata

Question: 113
Page: 168
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Arithmetic > Fractions >

Explanation: It's probably quicker to find the area of the unshaded regions than to find that of the shaded region. The width of the door is 6 feet, so after subtracting 1 foot of trim on each side, the width of the unshaded portion is 4 feet. The height is 8 feet, but three feet are occupied by trim, so the unshaded height is 5 feet. Thus, the area of the unshaded portion is wh = 4(5) = 20. The area of the entire door is wh = 6(8) = 48, so the area of the trim is the difference: 48 - 20 = 28. Thus, the fraction of the door that is covered by trim is (28/48) = (7/12), choice (D).

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