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In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Ab = 5.6 Cm, Ac = 6cm and Dc = 3cm, Find Bc. - CBSE Class 10 - Mathematics

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Question

In a ΔABC, AD is the bisector of ∠A, meeting side BC at D.

If AB = 5.6 cm, AC = 6cm and DC = 3cm, find BC.

Solution

We have, In ΔABC, AD is the bisector of ∠A.

We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

`therefore"BD"/"DC"="AB"/"AC"`

`rArr"BD"/3=5.6/6`

`rArr"BD"=(5.6xx3)/6=5.6/2=2.8 ` cm

⇒ BD = 2.8 cm

Since, BC = BD + DC

= 2.8 + 3

= 5.8 cm

∴ BC = 5.8 cm

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Solution In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Ab = 5.6 Cm, Ac = 6cm and Dc = 3cm, Find Bc. Concept: Angle Bisector.
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