Question

The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle. [ 3 Marks]

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, $\frac{AB}{AC}=\frac{BD}{DC}$ [ 1 Mark]
$\text{Therefore,}\frac{BD}{DC}=\frac{12}{18}=\frac{2}{3}$
So, BD and DC are in the ratio 2:3
i.e. , 2x + 3x = 20
5x = 20
x = 4 [ 1 Mark]
Therefore the lengths of the segments are :-
BD = 2x = 2(4) = 8 inches
DC = 3x =3(4) = 12 inches [ 1 Mark]