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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/DB = 3/4 and AC = 15 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 a 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/DB = 3/4 and AC = 15 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/BD = 3/4 and AC = 15 cm

    To find: Length of side AE

    By using Thales Theorem, we get

    AD/BD = AE/CE              – equation 1

    Let, AE = x

    Then CE = 15 – x.

    Now, putting values in equation 1,

    ⇒ 3/4 = x/ (15 – x)

    45 – 3x = 4x

    -3x – 4x = – 45

    7x = 45

    x = 45/7

    x = 6.43 cm

    ∴ AE= 6.43cm

    Therefore, Length of side AE is 6.43 cm

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