Question

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.

Answer 1

Let the shorter side of the rectangular field = x m.

Then its longer side = x + 30 m.

The diagonal of a rectangle is also the hypotenuse of the lower triangle Here the diagonal = x + 60 

∴ By Pythagoras Theorem 

(side)² + (side)² = (hypotenuse)² 

⇒ (x + 30)² + x² = (x + 60)² 

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

⇒ x² – 60x – 2700 = 0 

⇒ x² – 90x + 30x – 2700 = 0 

⇒ x(x – 90) + 30 (x – 90) = 0 

⇒ (x – 90) (x + 30) = 0 

⇒ x – 90 = 0 (or) x + 30 = 0 

⇒ x = +90 (or) x = -30 But ‘x’ can’t be negative. 

∴ x = 90 m 

i.e., the shorter side x = 90 m Longer side x + 30 = 90 + 30 = 120 m.