I finished what I started in my earlier post, same solution as Kenny M.

With side=2 as the base and h as the altitude, the other sides are b and c, but put b in terms of c since the problem asks for c.  So the sides are 2, c, and 4-2c.

x^2 + h^2 = (4-2c)^2

(2-x)^2 + h^2 = c^2

subtracting:

x = (1/4)(3c^2 - 16c + 20)

substitute into first equation:

16h^2 = -9c^4 + 96c^2 - 312c^2 + 384c -144

Take derivative:

32h*(dh/dc) = -36c^3 + 288c^2 - 624c + 384  (c=2 is a factor)

32h*(dh/dc) = (c-2)(-36c^2 + 216c - 192)

(-36c^2 + 216c - 192) = 0

c = 3 ± √33/3  reject the + version since c is part of a rope and the entire rope is 4.

Solution for c:  c = 3 - √33/3

c = 1.085145784487323780