# A line from a vertex of a triangle divides opposite side in a ratio,determine the ratio of areas?

In a triangle ABC,If a line drawn from vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?

I am thinking about using the property of similar triangles that if two triangles are similar than ratio of their areas is $=$ ratio of square of corresponding sides.

Let $AK$ be an altitude of $\Delta ABC$.
Thus, $$\frac{S_{\Delta ABD}}{S_{\Delta ADC}}=\frac{\frac{1}{2}BD\cdot AK}{\frac{1}{2}DC\cdot AK}=\frac{BD}{DC}=\frac{6}{3}=2$$