Advanced MathVery hardUniform frame width from equal areas
Advanced Math practice question
A rectangular photograph measuring 8 cm by 12 cm is mounted in a frame of uniform width w centimetres. The area of the frame alone is equal to the area of the photograph. What is the value of w?
Answer: 2
The outer rectangle is (8 + 2w) by (12 + 2w). Frame area = (8 + 2w)(12 + 2w) − 96 = 96, so 4w² + 40w − 96 = 0, w² + 10w − 24 = (w + 12)(w − 2) = 0. w = 2.
Common wrong answers
- If you answered 4
- 4 comes from using w instead of 2w for the added length on each dimension.
- If you answered 96
- 96 is the photograph's area, not a width.
- If you answered -12
- −12 is the rejected negative root.
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