In a triangle ABC,AB=6cm,AC=10cmand AD is the bisector of angle A. Find BD:DC
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Step-by-step explanation:
1:1.is the ratio.
they are equal
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Answer:
The length of BD is 2.5 cm and length of DC is 3.5 cm.
Given information: In triangle ABC, AD is the bisector of angle A, AB=10cm,AC=14cm,BC=6cm.
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Let BD=x, so DC=6-x.
Using angle bisector theorem, we get
AB/AC = BD/DC
10/4=x/6-x
5/7= x/6-x
On cross multiplication we get
5(6-x) = 7x
30-5x=7x
30=7x +5x
30= 12x
DIVIDE BOTH SIDE BY 12
30/12= x
2.5=x
DC=6-x=6-2.5=3.5
Step-by-step explanation:
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