- Jan 25, 2013
I will use geometry ,
maybe someone want to try it first
yes ,you got itI believe that the dashed lines in the diagram give a clue. They divide the triangle ABC into three smaller triangles, whose areas are $\frac12(12s)$, $\frac12(9(3s))$ and $\frac12(15s)$ (using Pythagoras to get the hypotenuse of triangle ABC as 15). The area of the whole triangle is $\frac12(9\times12)$. Equating that to the sum of the three smaller areas easily gives the equation $27s=54$ from which $s=2$.