Question

A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

Answer 1

Area of the rectangle = 180 sq metres
Let the length of the rectangle be 'l' m and breadth be 'b' m.
Three sides of the garden are fenced with 39 m of wire.

⇒$2b+l=39m$ [let the longest side is length]
⇒$l=(39-2b)m$
Therefore, Area $=l\times b=180$
$\Rightarrow b\times (39-2b)=180$
$\Rightarrow 2b^2-39b+180=0$

$\Rightarrow 2b^2-24b-15b+180=0$

$\Rightarrow 2b(b-12)-15(b-12)=0$

$\Rightarrow (b-12)(2b-15)=0$

$\Rightarrow b=12or\frac{15}{2}$

If the breadth of the garden is 12 m
Length of the garden $=l=(39-2\times 12)=15m$

If the breadth of the garden is $\frac{15}{2}m$
Length of the garden = $l=(39-2\times \frac{15}{2})=24m$