ABC is a triangle right-angled at A. Further, AB = 8 cm, BC = 10 cm. D is the point on BC such that AD is perpendicular to BC. What is ratio of area of triangle ADC to area of triangle ADB?

With AB = 8, AC = 6, BC = 10. Using the property that in a right triangle with altitude from the right angle to hypotenuse, BD = AB²/BC = 64/10 = 6.4 and DC = AC²/BC = 36/10 = 3.6. Triangles ADC and ADB share the same height AD, so their areas are in ratio DC : DB = 3.6 : 6.4 = 36 : 64 = 9 : 16.