Chapter 4: Quadratic Equations

Example – 16. Te diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 30 m more than the shorter side, find the sides of the field.

Solution :- Lt shorter side be x, then diagonal = x + 60 and longer side = x + 30

By Pythagoras Theorem, (x + 60)² = (x + 30)² + x². 

Or,     x² + 120x + 3600 = x² + 60x + 900 + x²
Or,     − x² + 60x + 2700 = 0
Or,     x² – 60x – 2700 = 0
Or,    (x – 90)(x + 30) = 0
Either,         x – 90 = 0     Or,     x + 30 = 0

Thus, x = 90 or, x = – 30. But length cannot be negative.

Hence shorter side = 90 m and longer side = 90 + 30 = 120 m.