AlgebraMediumGreatest integer length under a perimeter limit
Algebra practice question
A rectangle has a width of 5 centimetres, and its perimeter must be less than 40 centimetres. What is the greatest possible integer value of its length, in centimetres?
Answer: 14
Perimeter 2(5 + l) < 40 gives 5 + l < 20, so l < 15. The greatest integer less than 15 is 14. Check: 2(5 + 14) = 38 < 40.
Common wrong answers
- If you answered 15
- A length of 15 gives a perimeter of exactly 40, which is not LESS than 40.
- If you answered 30
- 30 is 40 − 2(5), forgetting to halve the remaining 30 for the two lengths.
- If you answered 35
- 35 is 40 − 5, forgetting that the perimeter counts each side twice.
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