In the following figure, ∠ABC = 90°, AB = (x + 8) cm, BC = (x + 1) cm and AC = (x + 15) cm. Find the lengths of the sides of the triangle.

In Δ ABC using Pythagoras theorem,

Hypotenuse² = Base² + Height²

⇒ AC² = AB² + BC²

⇒ (x + 15)² = (x + 8)² + (x + 1)²

⇒ x² + 225 + 30x = x² + 64 + 16x + x² + 1 + 2x

⇒ x² + 225 + 30x = 2x² + 65 + 18x

⇒ 2x² + 65 + 18x - x² - 225 - 30x = 0

⇒ x² - 12x - 160 = 0

⇒ x² - 20x + 8x - 160 = 0

⇒ x(x - 20) + 8(x - 20) = 0

⇒ (x - 20)(x + 8) = 0

⇒ x = 20 or -8

Length cannot be negative. So, x = 20.

AB = (x + 8) cm = (20 + 8) cm = 28 cm

BC = (x + 1) cm = (20 + 1) cm = 21 cm

AC = (x + 15) cm = (20 + 15) cm = 35 cm

Hence, the lengths of sides of the triangle are AB = 28 cm, BC = 21 cm and AC = 35 cm.