The Pythagorean would work if it were a straight line, but in reality it forms a curve called the "catenary".

The length of a catenary is:
S=2/a * sinh(L/2*a)

where S is your length, L is the distance between the ends, and a is a parameter defined as:

a = 8h/(S^2-4h^2)

This definition can't be solved for S in a closed form, so we have to approximate it mathematically with a computer. The result is about 50.84.

(The site for some reason insists that it's 50.85.)

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