In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD/DB = 2/3 and AC = 18 cm, Find AE.

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deepaksoniGuru

Asked: August 13, 20212021-08-13T16:26:32+05:30 2021-08-13T16:26:32+05:30In: CBSE

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.

Also it is given that AD/DB = 2/3 and AC = 18 cm,

Now we have to find the length of AE.

Understanding and learning CBSE maths
RD sharma, DHANPAT RAI publication

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AAREKH · Answer 1 · 2021-08-19T00:32:41+05:30

AAREKH Guru

Given:

Length of side AD/BD = 2/3 and AC = 18 cm

To find: Length of side AE.

By using Thales Theorem, we get

AD/BD = AE/CE – equation 1

Let, AE = x

Then CE = 18 – x

Now, putting values in equation 1,

⇒ 23 = x/ (18 – x)

3x = 36 – 2x

5x = 36 cm

x = 36/5 cm

x = 7.2 cm

∴ AE = 7.2 cm

Therefore, Length of side AE is 7.2 cm