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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 = 4 cm, AE = 8 cm, DB = x – 4 cm and EC = 3x – 19, find x.

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Question taken from RD sharma
Class 10th
Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions.

In this question we have a triangle ΔABC,

In which D and E are points on the sides AB and AC respectively such that DE || BC.

It is also given that AD = 4 cm, AE = 8 cm, DB = x – 4 cm and EC = 3x – 19,

Now we have to find x.

Understanding and learning CBSE maths
RD sharma, DHANPAT RAI publication

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1. Given:

Length of side AD = 4 cm, AE = 8 cm, DB = x – 4 and EC = 3x – 19

To Find: length of side x.

By using Thales Theorem, we get,

AD/BD = AE/CE                              – equation 1

Now, putting values in equation 1,

4/ (x – 4) = 8/ (3x – 19)

4(3x – 19) = 8(x – 4)

12x – 76 = 8(x – 4)

12x – 8x = – 32 + 76

4x = 44 cm

x = 11 cm

Therefore, Length of side x is 11 cm

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