Question

In figure, ∠AВC = 90°, AB : BD : DC = 3 : 1 : 3. If AC = 20 cm, then AD = ______.

Answer 1

In figure, ∠AВC = 90°, AB : BD : DC = 3 : 1 : 3. If AC = 20 cm, then AD = `underlinebb(4sqrt(10))`.

Explanation:

Let AB = 3x, BD = x, DC = 3x

So BC = BD + DC = 4x. 

In right triangle ABC (right-angled at B) AC = 5x (3-4-5 triangle).

So 5x = 20

⇒ x = 4 

In right triangle ABD (right angle at B) apply Pythagoras:

AD² = AB² + BD² 

= (3x)² + x²

= 10x²

So `AD = xsqrt(10)`

= `4sqrt(10)` cm