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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 = 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

 

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RD sharma, DHANPAT RAI publication

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1 Answer

  1. 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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