Question

Bimal wishes to start a $200m^2$ rectangular garden. since he has only $50m$ barbed wire, he fences three sides of the garden letting his house compound wall act as one of the longer sides of the garden. Find the dimensions of the garden.

Answer 1

Let the dimensions of the rectangular garden be $xm\times ym$

Then $xy=200$ since area is given as $200sq.m$

$\Rightarrow y=\frac{200}{x}$

The three sides of the rectangular garden is fenced with $50$ barbed wire $2x+y=50$

$\Rightarrow 2x+y=50$

$\Rightarrow 2x+\frac{200}{x}=50$

$\Rightarrow 2x^2-50x+200=0$

$\Rightarrow x^2-25x+100=0$

$\Rightarrow x^2-20x-5x+100=0$

$\Rightarrow x(x-20)-5(x-20)=0$

$\Rightarrow (x-20)(x-5)=0$

$\Rightarrow x=20or5$

When $x=20m,y=\frac{200}{20}=10m$

When $x=5m,y=\frac{200}{5}=40m$

Thus, the garden is of dimensions $20m\times 10m$ or $40m\times 5m$