Question

The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. cm) of this triangle is

(a) 24

(b) 72

(c) 48

(d) 144

Answer 1

(b) 72 cm²

Here s_m = \(\frac{9+12+15}{2}\) = 18 cm, where lengths of medians are m₁ = 9 cm, m₂ = 12 cm, m₃ = 15 cm.

∴ Area of triangle = \(\frac{4}{3}\sqrt{18(18-9)(18-12)(18-15)}\) cm²

= \(\frac{4}{3}\sqrt{18\times9\times6\times3}\) cm² = \(\frac{4}{3}\) x 9 x 6 cm² = 72 cm².