1. In an equilateral triangle the altitude bisects a side (divides it in 2), so if is the length of the side, by pythagoras we have:
(only the positive root because length is positive)
2. Let a be the altitude:
3. Let x be the height of the tree. Using similar triangles,
4. If the triangle is similar, then the sides must be in proportion with each other, but they can all be enlarged by a factor .
So by equating the sum of the sides of the enlarged triangle with its perimeter:
So the factor is 3, and hence the largest side is