AlgebraVery hardLengths satisfying a perimeter and an area condition
Algebra practice question
A rectangle has length L and width 4. Its perimeter must be at most 30, and its area must be at least 32. Which of the following describes the possible values of L?
- A. 8 ≤ L ≤ 11Correct
- B. L ≤ 11
- C. L ≥ 8
- D. 4 ≤ L ≤ 15
Answer: A. 8 ≤ L ≤ 11
2L + 8 ≤ 30 gives L ≤ 11, and 4L ≥ 32 gives L ≥ 8.
Why the other answers are wrong
- B. L ≤ 11
- This ignores the area condition.
- C. L ≥ 8
- This ignores the perimeter condition.
- D. 4 ≤ L ≤ 15
- These bounds come from neither condition.
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