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
Diagonal2= shorterside2+longerside2
Plug the values In this we get (x+60)2 = (x)2 + (x+30)2
= x2+x2+60x+900
(a+b)2=a2+b2+2ab
We get x2+120x+3600 = x2+x2+60x+900
x2+120x+3600 subtracting both side we get
0=x2−60x−2700
Factorize it now x2−90x+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