Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Answer 1

Let the base of the given right triangle be ‘x’ cm.

            ∴ Its height = (x – 7) cm

            

            Squaring both sides, we get

            169 = x² + (x – 7)²

            ⇒ 169 = x² + x² – 14x + 49

            ⇒ 14x + 49 – 169 = 0

            ⇒ 2x² – 14x – 120 = 0

            ⇒ x² – 7x – 60 = 0

            ⇒ x² – 12x + 5x – 60 = 0

            ⇒ x (x – 12) + 5 (x – 12) 0

            ⇒ (x–12) (x + 5) = 0

            Either x –12 = 0 ⇒ x=12

            or x + 5 = 0 ⇒ x = –5

            But the side of triangle can never be negative,

            ⇒ x = 12

            ∴ Length of the base = 12 cm

            ⇒ Length of the height = (12 – 7) cm = 5 cm

            Thus, the required base = 12 cm and height = 5 cm,