Question

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

∴ Maximum Area = x(20 – x)

= 10(20 – 10)

= 10 × 10

= 100 sq.m.