Question

A farmer wishes to grow a 100 m² rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.

Answer 1

Area of rectangular garden = 100 cm²
Length of barbed wire = 30 m
Let the length of the side opposite to wall = x

and length of other each side = `(30 - x)/(2)`
According to the condition,

`(x(30 - x))/(2)` = 100

⇒ x(30 - x) = 200
⇒ 30x - x² = 200
⇒ x² - 30x + 200 = 0
⇒ x² - 20x - 10x + 200 = 0
⇒ x(x - 20) - 10(x - 20) = 0
⇒ (x - 20)(x - 10) = 0
Either x - 20 = 0,
then x = 20
or 
x - 10 = 0,
then x = 10
(i) If x = 20,
then side opposite to the wal = 20m
and other side

= `(30 - 20)/(2)`

 = `(10)/(2)`
= 5m
(ii) If x = 10,
then side opposite to wall = 10m
and other side

= `(30 - 10)/(2)`

= `(20)/(2)`
= 10m
∴ Sides are 20m, 5m or 10m.