applying what sean said...
your 25' strings will become the hypotenuse of a right triangle. so pull out the high school geometry book...
if you recall the Pythagorean tTeorem: "a squared plus b squared equals c squared".
The trunk of the tree forms one side of the triangle: "a"...
The base of the nicely-shaped tree is 1/2 of the height... or a/2... but the tree creates 2 right triangles... so the other side of the triangle which is the radius or "b" is (a/2)/2
We get this:
(a*a) + (a/4 * a/4) = 25ft*25ft
solve for a (the trunk)... 24.25ft
solve for b (the radius)... 6.06ft
and the diameter is... 12.12ft
ok... Sean's answer was good enough. the kid's geometry book can stay on the shelf.
