Question

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

Answer 1

$\Rightarrow$ Let the shorter side be $xm$

$\Rightarrow$ Then, length of diagonal $=(x+60)m$

$\Rightarrow$ Length of longer side $=(x+30)m$

By applying Pythagoras theorem,

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

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

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

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

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

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

$\therefore$ $x=90$ and $x=-30$

Length can not be negative.

$\therefore$ $x=90$

$\Rightarrow$ The length of longer side $=x+30=90+30=120m$