Advanced MathHardWidth of a uniform frame
Advanced Math practice question
A rectangular photograph measures 8 by 10 inches. A frame of uniform width w inches surrounds it, and the photograph and frame together cover 168 square inches. What is the value of w?
Answer: 2
(8 + 2w)(10 + 2w) = 168 gives 4w² + 36w − 88 = 0, so w² + 9w − 22 = 0 and (w + 11)(w − 2) = 0. The width is 2.
Common wrong answers
- If you answered 4
- 4 is the total added to each dimension, 2w.
- If you answered 11
- 11 is the rejected root with its sign dropped.
- If you answered 88
- 88 is the frame's area.
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