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

Dear Student

Let us say, the shorter side of the rectangle bexm.
Then, larger side of the rectangle = (x+ 30) m

the length of the diagonal is = [ (x + 30)^2 + x^2 ]^(1/2) m
Given, diagonal= x+60

Therefore,

⇒x^2+(x+30)^2=(x+60)^2
⇒x^2+x^2+900+60x=x^2+3600+120x
⇒x^2- 60x- 2700 = 0
⇒x^2-90x+30x-2700=0
⇒x(x- 90) + 30(x-90) = 0
⇒(x- 90)(x+ 30) = 0
⇒x= 90, -30

Thanks