1. I've drawn a sketch of the worst case. (see attachment)

2. You get 2 similar triangles. Use proportions:

3. Use the Pythagorean theorem:

4. Replace y by the term of #2 and solve for h:

5. Differentiate h wrt x. Solve for x. You should come out with x = 36. Which means that the minimum value of h = 64.Spoiler: