AlgebraMediumRange of a side from a fencing limit and an area minimum
Algebra practice question
A rectangular plot has one side of length 12 metres. The plot must be enclosed with at most 60 metres of fencing and must have an area of at least 120 square metres. Which inequality describes all possible lengths w, in metres, of the other side?
- A. 10 ≤ w ≤ 18Correct
- B. 10 ≤ w ≤ 24
- C. w ≤ 18
- D. 10 < w < 18
Answer: A. 10 ≤ w ≤ 18
Fencing: 2(12 + w) ≤ 60 → w ≤ 18. Area: 12w ≥ 120 → w ≥ 10.
Why the other answers are wrong
- B. 10 ≤ w ≤ 24
- 24 comes from 12 + 2w ≤ 60, counting the 12-metre side only once.
- C. w ≤ 18
- Omits the area condition.
- D. 10 < w < 18
- Both bounds are inclusive.
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