Question

if three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

Answer 1

Let a and b be the two sides of a rectangle.

a + 2b = 400

Area of rectangle = ab (We have to maximize it)

b = (400-a)/2

Put the value of b in area of rectangle.

a(400-a)/2 = (400a-a^2)/2

On differentiating the above equation, we get

400-2a = 0 => a=200

b = 100

Area will be max when length of longer side = 200.

Answer: 200