A landscaper wishes to enclose a rectangular rest area with trees planted 1 meter apart along the boundary. The perimeter of the area is to be 120 meters. What will the maximum area of the rest area?

Answer 1

Suppose the rest area's length be x meters.

Perimeter = 2(length + widths)

So width = 120/2 - x = 60-x meter.

Area of the rest area A(x) = x(60-x) = -x²+60x = 30² -[x²-2x(30) +30²] = 900 -(x-30)²

[ Refer to section where you complete square to find min/max value of a quadratic eqn]

Maximum value of the quadratic A(x) is 900

Answer 2

perimiter=120

2x+2y=120

x+y=60

x=29

y=31

area=899