Advanced MathVery hardWidth of a border from the enlarged area
Advanced Math practice question
A rectangular photograph is 10 centimetres by 15 centimetres. A border of uniform width w centimetres is added around it, and the photograph with its border has an area of 300 square centimetres. What is the value of w?
Answer: 2.5 or 5/2
(10 + 2w)(15 + 2w) = 300 gives 4w² + 50w − 150 = 0, or 2w² + 25w − 75 = (2w − 5)(w + 15) = 0, so w = 2.5.
Common wrong answers
- If you answered 5
- 5 is 2w, the total added to each dimension.
- If you answered 150
- 150 is the area of the photograph alone.
- If you answered -15
- −15 is the negative root, not a width.
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