The lengths of three medians of a triangle are 3 cm, 6 cm and 5 cm. The area of the triangle is :

Correct option is C

Given:

Lengths of the medians: m₁ = 3 cm, m₂ = 6 cm, m₃ = 5 cm

Formula Used:

Area of a triangle = $$\frac{4}{3} \sqrt{s_m(s_m - m_1)(s_m - m_2)(s_m - m_3)}$$​​

where $$s_m = \frac{m_1 + m_2 + m_3}{2}$$​ is the semi-perimeter of the medians.

Solution:

Semiperimeter $$s_m = \frac{3 + 6 + 5}{2} = \frac{14}{2} = 7 \text{ cm}$$​​

Now,

Area = $$\frac{4}{3} \sqrt{7(7 - 3)(7 - 6)(7 - 5)}$$​​

​$$= \frac{4}{3} \sqrt{7 \times 4 \times 1 \times 2}$$​​

​$$= \frac{4}{3} \sqrt{56} \ \text{cm}^2$$​​