**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 14**

**14.** The perpendicular from A on side BC of a intersects BC at D such that DB = 3CD. Prove that

**Solution:**

**Given:**

AD BC and BD = 3CD.

**To Prove:**

**Proof: **

**L.H.S =**

{** by Pythagoras Theorem**}

**L.H.S =**

{ **by Pythagoras Theorem**}}

**L.H.S =**

** {BD = 3CD}**

L.H.S = ** (1)**

We have **BC = BD + CD = 3CD + CD = 4CD**

**(2)**

Putting **(2)** in** (1)**, we get

**L.H.S =** **= R.H.S**

**Hence Proved**