The three medians of a triangle measure 9 cm, 12 cm and 15 cm. A triangle's area is 4/3 of the area of the triangle whose sides are its three medians. Find the area of the original triangle in ${\text{cm}}^2$.

First build the triangle whose sides are the medians: 9, 12, 15 satisfies $9^2+12^2=81+144=225=15^2$, so it is right-angled and its area = ½ × $9\times 12=54{\text{cm}}^2$. The original triangle is 4/3 of that: $54\times 4/3=72{\text{cm}}^2.(54{\text{cm}}^2$ is the median triangle itself, one step short of the answer; turning the factor over, $54\times 3/4=40.5{\text{cm}}^2$, shrinks instead of grows — the original must be the LARGER of the two; $108{\text{cm}}^2$ doubles.)