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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 = x cm, DB = x – 2 cm, AE = x + 2 cm, and EC = x – 1 cm, find the value of x.

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Question drawn from very renowned book RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very important question of triangle.

In this question we have ΔABC,

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

Also it is given that  AD = x cm, DB = x – 2 cm, AE = x + 2 cm, and EC = x – 1 cm,

Now we have to find the value of x

learning CBSE maths in efficient way

RD sharma, DHANPAT RAI publication
Class 10th, triangle

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1. Given:

Length of side AD = x, DB = x – 2, AE = x + 2 and EC = x – 1

To find: Value of x.

By using Thales Theorem, we get

AD/BD = AE/CE                                       – equation 1

Now, putting values in equation 1,

x/(x – 2) = (x + 2)/(x – 1)

x(x – 1) = (x – 2)(x + 2)

2– x – x2 + 4 = 0

∴ x = 4

Therefore, the value of x is 4

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