In the given figure, AD = 13 cm, DC = 12 cm and BC = 3 cm, then AB is equal to :

1. 4 cm

2. 3 cm

3. 5 cm

4. 6 cm

In right angled △ DCB,

By pythagoras theorem,

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

⇒ BD² = DC² + BC²

⇒ BD² = (12)² + (3)²

⇒ BD² = 144 + 9

⇒ BD² = 153

⇒ BD = $\sqrt{153}$ cm.

In right angle △ ABD,

By pythagoras theorem,

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

⇒ AD² = AB² + BD²

⇒ 13² = AB² + $(\sqrt{153})^2$

⇒ 169 = AB² + 153

⇒ AB² = 169 - 153

⇒ AB² = 16

⇒ AB = $\sqrt{16}$ = 4 cm.

Hence, Option 1 is the correct option.