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In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D. If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

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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

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1 Answer

  1. 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

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