Question

The diagonal of a rectangular field is 60 metres more than shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Answer 1

We have,

Long side of rectangular field is 60 meters more then the shorter side.

Let the longer side will be $(y+30)mtr.$

And the length of the diagonal will be $(y+60)$ mtr.

Now, According to given question.

Using Pythagoras theorem,

${\left(Diagonal\right)}^2={\left(shorterside\right)}^2+{\left(longerside\right)}^2$

${(y+60)}^2=y^2+{(y+30)}^2$

$\Rightarrow y^2+3600+120y=y^2+y^2+900+60y$

$\Rightarrow 3600+120y-y^2-900-60y=0$

$\Rightarrow -y^2+60y+2700=0$

$\Rightarrow y^2-60y-2700=0$

$\Rightarrow y^2-(90-30)y-2700=0$

$\Rightarrow y^2-90y+30y-2700=0$

$\Rightarrow y(y-90)+30(y-90)=0$

$\Rightarrow (y-90)(y+30)=0$

If,

$y+30=0$

$y=-30\left(notpossible\right)$

If,

$y-90=0$

$y=90$

So, the length of shorter side $=y-30=90-39=60$

Longer side $90+30=120$

Hence, this is the answer.