#### 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.

#### Solution

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}

⇒ x^{2} + x^{2} - 14x + 49 = 169

⇒ 2x^{2} - 14x + 49 - 169 = 0

⇒ 2x^{2} - 14x - 120 = 0

⇒ 2(x^{2} - 7x - 60) = 0

⇒ x^{2} - 7x - 60 = 0

∴ The required quadratic equation is x^{2} - 7x - 60 = 0

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#### APPEARS IN

Solution 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. Concept: Quadratic Equations.