A gardener has 1080 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. Find the greatest area of the garden?
Answers
Given : A gardener has 1080 feet of fencing to fence in a rectangular garden.
One side of the garden is bordered by a river and so it does not need any fencing.
To Find : the greatest area of the garden
Solution:
Side bordered by river = y ft
other side = y feet
Hence fencing required = 2x + y ft
2x + y = 1080
=> y = 1080 - 2x
Area A = xy
=> A = x(1080 - 2x)
A = 1080x - 2x²
dA/dx = 1080 - 4x
dA/dx = 0 => 1080 - 4x = 0
=> x= 270
d²A/dx² = -4 < 0
Hence Area is maximum when x = 270
y = 1080 - 2x = 1080 - 2(270) = 540
so Area = xy = 270 * 540 = 1,45,800 sq feet
greatest area of the garden 1,45,800 sq feet
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