AlgebraHardPerimeter equation with a described relationship
Algebra practice question
A rectangle's length is 4 centimetres less than three times its width, and its perimeter is 64 centimetres. What is the width, in centimetres?
Answer: 9
Let the width be w; the length is 3w − 4. Perimeter: 2(3w − 4) + 2w = 64 → 8w − 8 = 64 → 8w = 72 → w = 9. Check: the length is 23, and 2(23) + 2(9) = 64.
Common wrong answers
- If you answered 7
- 7 comes from 8w − 8 = 64 solved as 8w = 56.
- If you answered 18
- 18 comes from using 4w for the perimeter: 4w − 8 = 64.
- If you answered 23
- 23 is the length, not the width.
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