A farmer has 64 feet of fence to enclose a rectangular vegetable garden which dimensions will result in the biggest

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01-06-2018
Mathematics

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A farmer has 64 feet of fence to enclose a rectangular vegetable garden which dimensions will result in the biggest

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tramserran tramserran · Answer 1 · 2018-06-01T11:26:44+02:00

Perimeter (P) = 2L + 2w
   64 = 2L + 2w
      64 - 2L = 2w
       32 - L = w

Area (A) = L x w
      = L x (32 - L)
    = 32L - L²

To find maximum area, calculate the derivative and set it equal to zero.

A' = 32 - 2L
0 = 32 - 2L
2L = 32
L = 16

Substitute L to solve for y: 32 - L = w → 32 - 16 = w → 16 = w

The maximum area will be 16 ft x 16 ft = 256 ft²