Question

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

Answer 1

Let the shorter side be $x$

then longer side will be$x+30$

and the diagonal will be $x+60$

now

${\left(x+60\right)}^2={\left(x+30\right)}^2+x^2\left[bypythagorustheorem\right]$

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

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

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

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

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

$\Rightarrow x=-30,x=90$

Since length of side cannot be negative

so $x=90m$

therefore shorter side=$90m$

longer side=$x+30$ = $90+30$=$120m$

Product of sides of the field $=90\times 120=10800$