MathNet 2016-part-03 — 184 problems (EN–VI) Question 49

The vertices of a triangle are at the points $(0,0)$, $(a, b)$, and $(2016-2a, 0)$, where $a\gt 0$. If $(a, b)$ is on the line $y=4x$, find the value(s) of $a$ that maximizes the triangle's area.