AlgebraVery hardGreatest side length under a fencing constraint
Algebra practice question
A gardener has 60 metres of fencing to enclose three sides of a rectangular plot against a wall. The side parallel to the wall must be at least twice as long as each side perpendicular to it. What is the greatest possible length, in metres, of a side perpendicular to the wall?
Answer: 15
With perpendicular sides x, the parallel side is 60 − 2x, and 60 − 2x ≥ 2x gives x ≤ 15.
Common wrong answers
- If you answered 12
- 12 uses 60 − 2x ≥ 3x.
- If you answered 20
- 20 uses 60 − 2x ≥ x.
- If you answered 30
- 30 halves the fencing and ignores the constraint.
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