A man who has 144 metres of fencing material wishes to enclose a rectangular garden. Find the maximum area he can enclose.

Let x be the length and y be the breadth of a rectangular garden and P be it's perimeter.

P=2(x+y)

144=2(x+y)

72=x+y

y=72-x…......(1)

If A is its area then,

A=x.y

A=x(72-x)

A=72x-x²

dA/dx = 72-2x

d²A/dx²= -2 (Max)

Since,

dA/dx = 0

72-2x=0

x=36m

y=72-x =72-36 =36m

Area= x * y = 36*36 =1296 m²