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# In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, Find AC.

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Question extracted from RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions. And has been asked in several times in exams.

In this question we have an triangle ΔABC,

In which D and E are points on the sides AB and AC respectively such that DE || BC.

Also it is given that AD = 6 cm, DB = 9 cm and AE = 8 cm

Now we have to find the length of AC

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1. Given: Δ ABC where

Length of side AD = 6 cm, DB = 9 cm, AE = 8 cm

Also, DE ∥ BC,

To find : Length of side AC

By using Thales Theorem we get, (As DE ∥ BC)

AD/BD = AE/CE    – equation 1

Let CE = x.

So then putting values in equation 1, we get

6/9 = 8/x

6x = 72 cm

x = 72/6 cm

x = 12 cm

∴ AC = AE + CE = 12 + 8 = 20.

Therefore, Length of side AC is 20 cm.

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