AlgebraMediumGreatest integer length under a perimeter limit
Algebra practice question
A rectangle has a width of 7 centimetres, and its perimeter must be less than 50 centimetres. What is the greatest possible integer length, in centimetres, of the rectangle?
Answer: 17
2(7 + L) < 50 → 7 + L < 25 → L < 18. The greatest integer less than 18 is 17.
Common wrong answers
- If you answered 18
- 18 gives a perimeter of exactly 50, which is not less than 50.
- If you answered 21
- 21 comes from 2L + 7 < 50, counting the width only once.
- If you answered 43
- 43 comes from 7 + L < 50, forgetting the factor of 2.
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