Question

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

Answer 1

Let the shorter side be $xm$

Then diagonal will be $x+60m$

The longer side will be $x+30m$

By Pythagoras theorem,

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

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

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

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

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

$\Rightarrow x=90,-30$

Neglecting negative value, we get
$x=90$
Shorter Side $=90m$
And longer Side $x+30=90+30=120m$

The shorter side is $90m$ and the longer side is $120m$ .