Question

A wire of length 36 meters is bent in the form of a rectangle. Find its dimensions if the area of the rectangle is maximum.

Answer 1

Let x metres and y metres be the length and breadth of the rectangle. 

Then its perimeter is 2(x + y) = 36

x + y = 18 y 

= 18 – x

Area of the rectangle = xy = x (18 – x)

∴ by the second derivative test, f has maximum value at x = 9. 

When x = 9, y = 18 – 9 = 9 

∴ x = 9 cm, y = 9 cm 

∴ the rectangle is a square of side 9 metres.