Question

The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

Answer 1

Let the shorter side be x m.

Length of the other side = (x + 30) m

Length of hypotenuse = (x + 60) m

Using Pythagoras theorem,

(x + 60)² = x² + (x + 30)²

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

x² – 60x – 2700 = 0

x² – 90x + 30x – 2700 = 0

x(x – 90) + 30(x – 90) = 0

(x – 90)(x + 30) = 0

x = 90, –30

But, x cannot be negative.

So, x = 90.

Thus, the sides of the rectangle are 90 m and (90 + 30) m = 120 m.