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 AD equal to?

In right triangle ABC with right angle at A, AB = 8 cm and BC (hypotenuse) = 10 cm. By Pythagoras, AC = √(100 − 64) = 6 cm. The area of triangle ABC = (1/2) × AB × AC = (1/2) × 8 × 6 = 24 sq cm. Also, area = (1/2) × BC × AD = (1/2) × 10 × AD. Equating, 5 × AD = 24, giving AD = 4.8 cm.