# 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.

120 m; 90 m

Let the shorter side be x

Longer side = x + 30

Diagonal = x + 60

Applying Pythagoras theorem

Diagonal2 = Longer side2 + shorter side2

(x + 60)2 = (x + 30)2 + x2

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

x2 - 60x - 2700 = 0

Performing factorization we get:

x2 - 90x + 30x - 2700 = 0

x(x - 90) + 30(x - 90) = 0

(x + 30)(x - 90) = 0

x = - 30, 90

Neglecting the negative term

Shorter Side = 90 m

Longer side = (90 + 30) = 120 m

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