# Math Help - Triangle optimization

1. ## Triangle optimization

An isoceles triangle has its vertex at the origin and its base parallel to the x-axis with the vertices above the axis on the curve y = -x^2 + 27. What is the largest area the triangle can have?

I know what the picture looks like, but that's about it..

2. We may use the triangle area formula

$A=\frac{1}{2}bh=\frac{1}{2}\cdot 2x\cdot (27-x^2)\;\;\;\;\;\;\;\;\;\;\; 0\le x\le 3\sqrt{3}$

together with the symmetry of the graph of $y=27-x^2$.