Triangle ABC is right-angled at B, with $AB = 9$ cm and $BC = 12$ cm. D is the point on AC such that BD is perpendicular to AC. What is DC?

Explanation

1. 01

   AC = $\sqrt{9^2 + 12^2} = 15$ cm.

2. 02

   Triangles BDC and ABC are similar (they share $\angle C$ and each has a right angle), so $\frac{DC}{BC} = \frac{BC}{AC}$.

3. 03

   $DC = \frac{12^2}{15} = \frac{144}{15} = 9.6$ cm.