Question

A farmer wishes to grow a $100m^2$ rectangular vegetable garden. He has only $30m$ barbed wire, so he fences three sides of the rectangular garden letting the compound wall of his house act as the fourth side fence. Find the dimensions of his garden.

Answer 1

Let the length of one side be $x$ metres and the other side be $y$ metres.

Here one side is a compound wall and 30 m wire is used for fencing.

$\Rightarrow x+y+x=30$

$\Rightarrow y=30-2x$

Area of the vegetable garden $=100m^2$

$\Rightarrow$ $xy=100$

$\Rightarrow x(30-2x)=100$

$\Rightarrow 30x-2x^2=100$

$\Rightarrow 15x-x^2=50$

$\Rightarrow x^2-15x+50=0$

$\Rightarrow x^2-10x-5x+50=0$

$\Rightarrow (x-10)(x-5)=0$

$\Rightarrow x=5,10$

When $x=5$ we have
$y=30-(2\times 5)=20$

When $x=10$,we have
$y=30-(2\times 10)=10$

Hence, the dimensions of the vegetable garden are $5m\times 20m$ or $10m\times 10m$