Question

A person wishes to make a 100 sq. m rectangular garden. Since he has only 30 m barbed wire for fencing, he fences only three sides letting the house wall act as the fourth side. The width of the garden is

• A. $10m$
• B. $5m$
• C. $50m$
• D. $100m$

Answer 1

Answer: (B)

$5m$

Area of the garden $=100m^2$

Or, $l\times b=100$

Or, $l=\frac{100}{b}$

Given that, the garden is fenced on three sides.

Hence, length of fencing $=2b+l=30$

$\Rightarrow \frac{200}{l}+l=30$

$\Rightarrow l^2-30l+200=0$

$\Rightarrow l^2-20l-10l+200=0$

$\Rightarrow l(l-20)-10(l-20)=0$

$\Rightarrow (l-20)(l-10)=0$

Hence, $l=20or10$

Or, $b=\frac{100}{20}=5or\frac{100}{10}=10$

Since, the garden is in the shape of a rectangle, the length and breadth cannot be equal.

Therefore, the length and the breadth of the garden are $20m$ and $5m$ respectively.

Hence, the width of the rectangular garden is $5m$.