TITLE: How to find area of triangle from its medians
QUESTION [16 upvotes]: The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is
a) $48$
b) $144$
c) $24$
d) $72$
I don't want whole solution just give me the hint how can I solve it.Thanks.

REPLY [2 votes]: There exists a formulae giving the area of a triangle in function of its medians. It is
$$A=\frac13\sqrt{2\alpha^2\beta^2+2\beta^2\gamma^2+2\gamma^2\alpha^2-\alpha^4-\beta^4-\gamma^4}$$ where it is clear what are $\alpha,\beta$ and $\gamma$.