AlgebraMediumRange of a side from a perimeter limit and an area minimum
Algebra practice question
A square must have a perimeter of at most 60 centimetres and an area of at least 100 square centimetres. Which inequality describes all possible side lengths s, in centimetres?
- A. 10 ≤ s ≤ 15Correct
- B. 10 < s < 15
- C. s ≤ 15
- D. 100 ≤ s ≤ 60
Answer: A. 10 ≤ s ≤ 15
4s ≤ 60 gives s ≤ 15, and s² ≥ 100 gives s ≥ 10: 10 ≤ s ≤ 15.
Why the other answers are wrong
- B. 10 < s < 15
- Both limits are inclusive.
- C. s ≤ 15
- Omits the area condition.
- D. 100 ≤ s ≤ 60
- Those are the limits on perimeter and area, not on s.
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