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deepaksoni
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Asked: 2021-08-14T15:01:35+05:30 In:

In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.

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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.

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

 

learning CBSE maths in effective way.
RD sharma, DHANPAT RAI publication

chapter 4class 10thexercise 4.2rd sharmatriangles
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    1 Answer

    1. Guru

      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

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