Question

A rectangle has a perimeter of 80 cm. If its width is x, express its length and its area in terms of x. What is the maximum area of the rectangle?

Answer 1

2x + 2l = 80
2l = 80 - 2x
l = (80 - 2x)/2
= 40 - x
A = Area = l*x
= (40 - x)*x
= 40x - x^2

dA/dx = 40 - 2x
dA/dx = 0 = 40 - 2x
2x = 40
x = 40/2
= 20

l = 40 - x
= 40 - 20
= 20

max area = 20*20 = 400 cm^2

Ans. 400 cm^2