**Solution:**

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} = x^{2}+(x+30)^{2}

x^{2}-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**