Question

The medians of a $\triangle$ABC are 9 cm, 12 cm and 15 cm respectively. Then the area of the $\triangle$ABC

Answer 1

72 cm$^2$

Answer 2

The area of a triangle ($A$) is related to the area of the triangle formed by its medians ($A_m$) by the formula $A = \frac{4}{3} A_m$. Given medians 9 cm, 12 cm, 15 cm, we recognize that these lengths form a right-angled triangle ($9^2 + 12^2 = 15^2$). The area of this right-angled triangle ($A_m$) is $\frac{1}{2} \times 9 \times 12 = 54 \text{ cm}^2$. Substituting this into the formula, the area of $\triangle$ABC is $\frac{4}{3} \times 54 = 72 \text{ cm}^2$.