UPSC CDS 2 2021 Math Paper

Concept:Area of a triangle remains the same regardless of which base and corresponding altitude are used.Explanation:The triangle has sides $AB = 6$ cm, $BC = 10$ cm, and $CA = 8$ cm.It is a right‑angled triangle with the right angle at vertex A because $6^2 + 8^2 = 36 + 64 = 100 = 10^2$.Area using legs $AB$ and $AC$: $\frac{1}{2} \times 6 \times 8 = 24$ cm$^2$.Let $AD$ be the altitude from vertex A to side BC.Area using base $BC$: $\frac{1}{2} \times 10 \times AD$.Equating the two area expressions: $\frac{1}{2} \times 10 \times AD = 24$.Simplifying: $5 \times AD = 24$, so $AD = \frac{24}{5} = 4.8$ cm.Answer:$4.8$ cm (Option D).