Question

The altitude of a right angled triangle is 7 cm less than its base. If its hypotenuse is 17 cm long, then represent the above information in the form of a quadratic equation.

Answer 1

Let the base of triangle = x cm

Then, its altitude = (x − 7) cm

Hypotenuse of triangle = 17 cm  ...[Given]

By Pythagoras theorem, we have

P² + B² = H²

(x − 7)² + x² = (17)²

∴ x² − 14x + 49 + x² = 289  ...[∵ (a − b)² = a² − 2ab + b²]

∴ 2x² − 14x + 49 - 289 = 0

∴ x² − 7x − 120 = 0,  

which is the required quadratic equation.