In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.

By formula,

By pythagoras theorem,

⇒ (Hypotenuse)² = (Perpendicular)² + Base²

Let CD be x cm.

In right angle triangle ACD,

By pythagoras theorem,

⇒ AC² = AD² + CD²

⇒ 6² = AD² + x²

⇒ 36 = AD² + x²

⇒ AD² = 36 - x² ……..(1)

In right angle triangle ABD,

By pythagoras theorem,

⇒ AB² = AD² + BD²

⇒ 16² = AD² + (BC + CD)²

⇒ 256 = 36 - x² + (12 + x)² [From equation (1)]

⇒ 256 = 36 - x² + 12² + x² + 2(12)x

⇒ 256 = 36 + 144 + 24x

⇒ 256 = 180 + 24x

⇒ 24x = 256 - 180

⇒ 24x = 76

⇒ x = $\dfrac{76}{24} = \dfrac{19}{6} = 3\dfrac{1}{6}$ cm.

Hence, CD = $3\dfrac{1}{6}$ cm.