This is LaTeX code:

[latex]
s=\frac{13+14+15}{2}=21\\P=\sqrt{21(21-14)(21-13)(21-15)}=\sqrt{21\cdot7\cdot8\cdot6}=84cm^2\\P_{\triangle{ABC}}=\frac{1}{2}(14\cdot r)+\frac{1}{2}(13\cdot r)=84\\\frac{1}{2}r(14+13)=84\\r=\frac{168}{27}=\frac{56}{9}cm
[/latex]