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 an 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 = 6 cm, DB = 9 cm and AE = 8 cm
Now we have to find the length of AC
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RD sharma, DHANPAT RAI publication
Given: Δ ABC where
Length of side AD = 6 cm, DB = 9 cm, AE = 8 cm
Also, DE ∥ BC,
To find : Length of side AC
By using Thales Theorem we get, (As DE ∥ BC)
AD/BD = AE/CE – equation 1
Let CE = x.
So then putting values in equation 1, we get
6/9 = 8/x
6x = 72 cm
x = 72/6 cm
x = 12 cm
∴ AC = AE + CE = 12 + 8 = 20.
Therefore, Length of side AC is 20 cm.