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 length of the shorter side be x metres.

Thus the length of the longer side=(x+30) m

Length of the diagonal=(x+60)m

Each angle of a rectangle=90 degrees

By Pythagoras Theorem, (diagonal)²=(shorter side)²+(longer side)²

(x+60)²  = x²+(x+30)²

x²-60x-2700=0  => (x+30)(x-90)=0  => x=-30 or x=90

As the length of a side cannot be negative,the length of the shorter side = 90 m.

Thus the length of the longer side=120 m