In ΔABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is:

The correct option is 2 : 1.

Step-by-step explanation:

Given that in triangle ΔABC, AD is the internal bisector of ∠A, meeting side BC at D.

We are given the lengths:

$BD=5\text{cm}$

$BC=7.5\text{cm}$

First, calculate the length of segment DC:

$DC=BC-BD$

$DC=7.5-5=2.5\text{cm}$

According to the Angle Bisector Theorem, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle. Therefore:

$\frac{AB}{AC}=\frac{BD}{DC}$

Substituting the given values into the ratio:

$\frac{AB}{AC}=\frac{5}{2.5}=\frac{2}{1}$

Hence, the ratio AB : AC is $2:1$.