Question

Please help me solve
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 272ft of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Answer 1

2w + l = 272 ft
----> l = -2w + 272
=> A = w ( -2w + 272)
= - 2w² + 272w

The largest area happens when A' = 0
A' = - 4w + 272 = 0
---> w = 272/4 = 68 ft
==> l = -2* 68 + 272 = 136 ft

Thus largest area can be enclosed:
A = 68 * 136 = 9248 ft²

Answer 2

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