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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.

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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  = 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

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