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Solution for In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Ad = 5.6 Cm, Bc = 6cm and Bd = 3.2 Cm, Find Ac. - CBSE Class 10 - Mathematics

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Question

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

If AD = 5.6 cm, BC = 6cm and BD = 3.2 cm, find AC.

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 containing the angle.

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

`5.6/"AC"=3.2/(6-3.2)`     [∵ DC = BC – BD]

`rArr5.6/"AC"=3.2/2.8`

`rArr"AC"=(5.6xx2.8)/3.2`

`=(5.6xx7)/8=0.7xx7`

= 4.9 cm

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Solution In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Ad = 5.6 Cm, Bc = 6cm and Bd = 3.2 Cm, Find Ac. Concept: Angle Bisector.
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