Question

In figure, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = ______ and AB = ______.

Answer 1

In figure, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then BD = `underlinebb(2sqrt(5)  cm)` and AB = 6 cm.

Explanation:

AC = AD + CD

= 4 + 5

= 9 cm

Using the altitude-to-hypotenuse relations from similarity of the right-triangle pieces: 

BD² = AD × CD and AB² = AD × AC.

So, BD² = 4 × 5 = 20 

⇒ BD = `sqrt(20)`

⇒ BD = `2sqrt(5)` cm

AB² = 4 × 9

= 36 

⇒ AB = 6 cm