A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is :

Solution (By Examveda Team)

We have :
$$\eqalign{ & 2b + l = 30 \cr & \Rightarrow l = 30 - 2b \cr} $$
$$\eqalign{ & {\text{Area}} = {\text{100 }}{m^2} \cr & \Rightarrow l \times b = 100 \cr & \Rightarrow b\left( {30 - 2b} \right) = 100 \cr & \Rightarrow {b^2} - 15b + 50 = 0 \cr & \Rightarrow \left( {b - 10} \right)\left( {b - 5} \right) = 0 \cr & \Rightarrow b = 10{\text{ or }}b = 5 \cr} $$
When, b = 10, $$l$$ = 10 and when b = 5, $$l$$ = 20
Since the garden is rectangular, so its dimension is 20 m × 5 m