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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
⇒ 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
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