AlgebraHardLongest plot from a fixed length of fence
Algebra practice question
A gardener has 60 metres of fencing to enclose a rectangular plot, one side of which is 12 metres. What is the greatest possible length, in metres, of the adjacent side?
Answer: 18
Perimeter 2(12 + w) ≤ 60, so 12 + w ≤ 30 and w ≤ 18. The greatest length is 18, using all 60 metres.
Common wrong answers
- If you answered 24
- 24 is 60 − 36, a slip; the two remaining sides share 36 metres, so each is 18.
- If you answered 36
- 36 is 60 − 2(12), forgetting to halve the remaining 36 between the two unknown sides.
- If you answered 48
- 48 is 60 − 12, forgetting that both 12-metre sides and both unknown sides need fencing.
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