Using the Pythagoren Theorem, we can create two equations for the trapezoid height.
hgt^{2} = 15^{2} -L^{2} *or* hgt^{2} = 225 -L^{2}

hgt^{2} = 20^{2} -R^{2} *or* hgt^{2} = 400 -R^{2}

Since the right side of both equations = hgt^{2}, we can state that both equations equal each other:

225 -L^{2} = 400 -R^{2} *or*

a) L^{2} = R^{2} -175

We know that L + R + 30 = 55 so, we can create 2 more equations:

L = 25 -R *and* R = 25 -L

If we square *L = 25 -R* we get the equation:

b) L^{2} = R^{2} -50R +625

Since the right side of equations 'a' and 'b' equal L^{2}, we can state that:

R^{2} -175 = R^{2} -50R +625

50R = 800

R = 16