Question

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

Answer 1

Given that in a right triangle is 7cmless than its base

Let base of the triangle be denoted by x

⇒ Height of the triangle = (x - 7)cm

We have hypotenuse of the triangle = 13cm

We know that, in a right triangle

(base)² + (height)² = (hypotenuse)²

⇒ (x)² + (x - 7)² = (13)²

⇒ x² + x² - 14x + 49 = 169

⇒ 2x² - 14x + 49 - 169 = 0

⇒ 2x² - 14x - 120 = 0

⇒ 2(x² - 7x - 60) = 0

⇒ x² - 7x - 60 = 0

∴ The required quadratic equation is x² - 7x - 60 = 0.