Question

A farmer has $70m$ of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is $600sqm$, find the length of its shorter side.

Answer 1

Let the length of rectangle is $=l$

And breadth of rectangle$=b$

So,

Area of rectangle$=l\times b$

$l\times b=600$

Now, According to given question,

$2l+b=70$

$\Rightarrow 2l+\frac{600}{l}=70$

$\Rightarrow 2l-70+\frac{600}{l}=0$

$\Rightarrow 2l^2-70l+600=0$

$\Rightarrow 2l^2-40l-30l+600=0$

$\Rightarrow 2l(l-20)-30(l-20)=0$

$\Rightarrow (l-20)(2l-30)=0$

$\Rightarrow l-20=0,2l-30=0$

$\Rightarrow l=20mtrorl=15mtr$

If $l=20mtr$ then, $b=30mtr.$

If $l=15mtr.$ then,$b=40mtr.$

Hence ,this is the required answer.