2015 AMC 12B Problem 11

The line 12x+5y=60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?

\textbf{(A)}\; 20 \qquad\textbf{(B)}\; \dfrac{360}{17} \qquad\textbf{(C)}\; \dfrac{107}{5} \qquad\textbf{(D)}\; \dfrac{43}{2} \qquad\textbf{(E)}\; \dfrac{281}{13}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.