AlgebraHardGreatest length under a perimeter limit
Algebra practice question
A rectangle's width is 3 centimetres less than its length, and its perimeter is at most 30 centimetres. What is the greatest possible length of the rectangle, in centimetres?
Answer: 9
With length l and width l − 3: 2(l + l − 3) ≤ 30, so 4l − 6 ≤ 30, 4l ≤ 36, l ≤ 9. The greatest length is 9 (giving a 9 by 6 rectangle with perimeter 30).
Common wrong answers
- If you answered 6
- 6 is the WIDTH when the length is 9.
- If you answered 12
- 12 comes from l + (l − 3) ≤ 30 (forgetting the factor 2), giving a perimeter of 42.
- If you answered 7.5
- 7.5 is 30/4, ignoring the 3-centimetre difference.
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