AlgebraVery hardRectangle whose area survives a reshaping
Algebra practice question
A rectangle has a perimeter of 40 centimetres. If its length is decreased by 3 centimetres and its width is increased by 3 centimetres, its area does not change. What is the length of the original rectangle, in centimetres?
Answer: 11.5 or 23/2
L + W = 20 and (L − 3)(W + 3) = LW. Expanding the second: 3L − 3W − 9 = 0, so L − W = 3. Adding to L + W = 20 gives 2L = 23, L = 11.5.
Common wrong answers
- If you answered 10
- 10 assumes a square, but then the area would change.
- If you answered 13
- 13 comes from L − W = 6, forgetting to divide 9 by 3 correctly.
- If you answered 8.5
- 8.5 is the width.
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