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.

We have 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 = 2 cm, AB = 6 cm and AC = 9 cm,

Now we have to find AE

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RD sharma, DHANPAT RAI publication

Given:Length of side AD = 2 cm, AB = 6 cm and AC = 9 cm

To find: Length of side AC.Length of DB = AB – AD = 6 – 2 = 4 cm

By using Thales Theorem, we get

AD/BD = AE/CE – equation 1

Now, putting values in equation 1,

2/4 = x/(9 – x)

4x = 18 – 2x

6x = 18

x = 3 cm

∴ AE = 3cm

Therefore, Length of side AE is 3 cm