Question

The diagonal of a rectangular field is 40 meters more than the shorter side. If longer side is 20 meters more than the shorter side, find the sides of the field.

Answer 1

Given that diagonal of a rectangular field is $60$ metres more than the shorter side
So diagonal will = $x+60m$
Given that the longer side is $30$ metres more than the shorter side =Longer side = $x+30m$
All angles in rectangle is always = $90$
so that we can Use Pythagoras theorem
$Diagona{l}^2$= $shortersid{e}^2+longersid{e}^2$
Plug the values In this we get $(x+60{)}^2$ = $(x{)}^2$ + $(x+30{)}^2$
= $x^2+x^2+60x+900$
$(a+b{)}^2=a^2+b^2+2ab$
We get $x^2+120x+3600$ = $x^2+x^2+60x+900$
$x^2+120x+3600$ subtracting both side we get
$0=x^2-60x-2700$
Factorize it now $x^2-90x+30x-2700=0$
$x(x-90)+30(x-90)=0$
$(x-90)(x+30)=0$
$x-90=0orx+30=0$
$x=90$ or $x=-30$
Any side of rectangle cannot negative
so shorter side = $x+30=90+30=120$ m
Diagonal is = $x+60=90+60=150$ m