Question

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:

• A. 10 m × 10 m
• B. 20 m × 5 m
• C. 30 m × 3.33 m
• D. 40 m × 2.5 m
• E. None of these

Answer 1

The correct option is B

20 m × 5 m

We have: 2b + l = 30 $\Rightarrow$ l = 30 - 2b

Area = 100 m${}^2$ $\Rightarrow$ l $\times$ b = 100 $\Rightarrow$ b (30 -- 2b) = 100 $\Rightarrow$ b${}^2$ -- 15b + 50 = 0

$\Rightarrow$ (b -- 10) (b -- 5) = 0 $\Rightarrow$ b = 10 or b = 5

When b = 10, l = 10 and when b = 5, l = 20.

Since the garden is rectangular, so its dimension is 20 m $\times$ 5 m.