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

Solution:

Let us say, the shorter side of the rectangle be x m.


Then, larger side of the rectangle = (x + 30) m


Diagonal of the rectangle = √[x2+(x+30)2] As given, the length of the diagonal is = x + 60 m


⇒ x2 + (x + 30)2 = (x + 60)2


⇒ x2 + x2 + 900 + 60x = x2 + 3600 + 120x


⇒ x2 – 60x – 2700 = 0


⇒ x2 – 90x + 30x – 2700 = 0


⇒ x(x – 90) + 30(x -90)


⇒ (x – 90)(x + 30) = 0


⇒ x = 90, -30