, 2003

Solution:

The answer is (E). With reference to the figure alongside, we have that the area of the equilateral triangle with unknown side $l$ can be determined in two ways:

1) as the sum of the areas of three triangles with base $l$ and heights $5, 7, 8$

2) with the usual area formula, keeping in mind that the height of an equilateral triangle is $l \frac{\sqrt{3}}{2}$.

We thus have $\frac{l \cdot (5+7+8)}{2} = \frac{1}{2} l^{2} \frac{\sqrt{3}}{2}$, from which $l = \frac{40}{3} \sqrt{3}$.