Question taken from RD sharma
Class 10th
Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.3
This is very basic and important questions.
It is given that In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D
Also If AB = 10 cm, AC = 6 cm and BC = 12 cm,
Now we have to find BD and DC
Understanding and learning CBSE maths
RD sharma, DHANPAT RAI publication
Since, AD is the bisector of ∠ A meeting side BC at D in Δ ABC
⇒ AB/ AC = BD/ DC
10/ 6 = BD/ DC …….. (i)
And, we know that
BD = BC – DC = 12 – DC
Let BD = x,
⇒ DC = 12 – x
Thus (i) becomes,
10/ 6 = x/ (12 – x)
5(12 – x) = 3x
60 -5x = 3x
∴ x = 60/8 = 7.5
Hence, DC = 12 – 7.5 = 4.5cm and BD = 7.5 cm