The altitude of a triangle is 6 cm more than its base. If its area is 108 cm 2 , find the base and height of the triangle.

Let the base of triangle = x cm ∴ Altitude of triangle = ( x + 6 ) cm We know that, Area of triangle = 1 2 × base × height ⇒ 108 = 1 2 × x × ( x + 6 ) ⇒ x 2 + 6 x - 216 = 0 ⇒ x 2 + 18 x - 12 x - 216 = 0 ⇒ x ( x + 18 ) - 12 ( x + 18 ) = 0 ⇒ ( x - 12 ) ( x + 18 ) = 0 Now if x - 12 = 0 then x = 12 and if x + 18 = 0 then x = - 18 Since base of triangle can not be negative. Therefore, x = 12 . Hence, height of triangle = 12 + 6 = 18 cm