Question

A person wishes to make a $100m^2$ rectangular garden. Since he has only $30m$ 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

The correct option is B $5m$

Given, Area of rectangular garden $=100m^2$
$l\times b=100$ $\left(1\right)$
Wire used for fencing three sides or Perimeter of $3$ sides of garden $=30m$
$b+l+b=30$
$\Rightarrow 2b+l=30$ $\left(2\right)$
Putting value of $l$ from $\left(2\right)$ in $\left(1\right)$, we get
$b(30-2b)=100$
$\Rightarrow 2b^2-30b+100=0$
$\Rightarrow b^2-15b+50=0$
On solving the quadratic equation by splitting the middle term, we get
$b=5,10$
If $b=10$, then we get $l=10$, which is not possible, as it is a rectangular garden.
so we take $b=5\Rightarrow l=20$
So, the width of the rectangular garden is $5m$.