UPSC CDS I 2025 Mathematics Paper

Concept:In a right triangle, the altitude from the right angle to the hypotenuse equals the product of the legs divided by the hypotenuse.Explanation:Triangle ABC is right‑angled at A, with AB = 8 cm, BC = 10 cm, and AD perpendicular to BC.Find AC using Pythagoras: AC² = BC² − AB² = 100 − 64 = 36, so AC = 6 cm.Now apply altitude formula: AD = (AB × AC) ÷ BC = (8 × 6) ÷ 10 = 48 ÷ 10 = 4.8 cm.Answer:4.8 cm, which corresponds to option A.