Question extracted from RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.3
This is very basic and important questions. And has been asked in several times in exams.
In this question it is given that In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D.
Also it is given that AB = 10 cm, AC = 14 cm and BC = 6 cm,
Now we have to find the length of BD and DC.
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RD sharma, DHANPAT RAI publication
Given: In Δ ABC, AD is the bisector of ∠A meeting side BC at D. And, AB = 10 cm, AC = 14 cm, and BC = 6 cm
Required to find: BD and DC.
Since, AD is bisector of ∠A
We have,
AB/AC = BD/DC (AD is bisector of ∠ A and side BC)
Then, 10/ 14 = x/ (6 – x)
14x = 60 – 6x
20x = 60
x = 60/20
∴ BD = 3 cm and DC = (6 – 3) = 3 cm.