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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 = 2.5 cm, BD = 3.0 cm, and AE = 3.75 cm, find the length of 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 been given the 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 = 2.5 cm, BD = 3.0 cm, and AE = 3.75 cm,

Now we have to find the length of AC

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RD sharma, DHANPAT RAI publication

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1. Given:

Length of side AD = 2.5 cm, AE = 3.75 cm and BD = 3 cm

To find : Length of side AC

By using Thales Theorem, we get

AD/BD = AE/CE                              – equation 1

Now, putting values in equation 1,

We get,

2.5/ 3 = 3.75/ CE

2.5 x CE = 3.75 x 3

CE = 3.75×32.5

CE = 11.252.5

CE = 4.5

Now, AC = 3.75 + 4.5

∴ AC = 8.25 cm.

Therefore, the value of AC is 8.25cm

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