Carol has 2400 ft of fencing to fence in a rectangular horse

Carol has 2400 ft of fencing to fence in a rectangular horse corral.
Find a function that models the area of the corral in terms of the width of x of the corral.
Find the dimensions of the rectangle that maximize the area of the corral.

Solution

Perimeter of Corral = 2(length +width ) = 2400

length + x = 1200

Therefore, Length = 1200-x

Area of Corral = length * width = (1200-x)*x

A(x)= 1200x - x²

Area of a rectangle is maximum when it becomes a square.

Therefore, Perimeter of square = 4*side = 2400

Side = 600 ft

Hence, dimension = 600 ft.