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Altitudes of a Triangle

Source: 2015 amc 10b #13

February 26, 2015
analytic geometryAMC

Problem Statement

The line 12x+5y=6012x+5y=60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle? <spanclass=′latex−bold′>(A)</span>20<spanclass=′latex−bold′>(B)</span>36017<spanclass=′latex−bold′>(C)</span>1075<spanclass=′latex−bold′>(D)</span>432<spanclass=′latex−bold′>(E)</span>28113<span class='latex-bold'>(A) </span> 20 \qquad<span class='latex-bold'>(B) </span> \dfrac{360}{17} \qquad<span class='latex-bold'>(C) </span> \dfrac{107}{5} \qquad<span class='latex-bold'>(D) </span> \dfrac{43}{2} \qquad<span class='latex-bold'>(E) </span> \dfrac{281}{13}
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