Question

A garden is to be laid out in a rectangular area and protected by wire fence. What is the largest possible area of the fenced garden with 40 metres of wire.

Answer 1

Perimeter = 40 m

2(l + b) = 40 ⇒ l + b = 20 

Let l = x m 

b = (20 – x)m 

Area = l × b = x(20 – x) = 20x – x² 

To find the maximum area 

A(x) = 20x – x² 

A'(x) = 20 – 2x 

A”(x) = -2 

A'(x) = 0 ⇒ 20 – 2x = 0 

⇒ x = 10 

x = 10 is a maximum point 

Therefore, maximum area = x(20 – x)

= 10(20 – 10) 

= 10 × 10 = 100 sq.m.