Question

The largest angle of a triangle, whose sides are 12 cm, 18 cm, and 20 cm, is bisected.
Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

Answer 1

Since the largest side measures 20 inches, the largest angle is angle A and hence angle A is bisected.
According to Angle Bisector Theorem, $\frac{AB}{AC}=\frac{BD}{DC}$
$\text{Therefore,}\frac{BD}{DC}=\frac{12}{18}=\frac{2}{3}$
So, BD and DC are in the ratio 2:3.
i.e. , 2x + 3x = 20
5x = 20
x = 4 cm
Therefore the lengths of the segments are:
BD = 2x = 2(4) = 8 cm
DC = 3x =3(4) = 12 cm