Advanced MathHardRectangle whose area is unchanged after resizing
Advanced Math practice question
A rectangle's length is twice its width. If the width is increased by 2 units and the length is decreased by 3 units, the area is unchanged. What is the width of the original rectangle?
Answer: 6
Original area: 2w · w = 2w². New area: (w + 2)(2w − 3) = 2w² + w − 6. Setting them equal: 2w² = 2w² + w − 6 → w = 6.
Common wrong answers
- If you answered 3
- 3 comes from setting w − 6 = −3 or halving 6.
- If you answered 12
- 12 is the original length.
- If you answered -6
- −6 has the wrong sign: w − 6 = 0.
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