Suppose ABCD is an isosceles trapezoid with bases AB and CD and sides AD and BC such that CD > AB. Also suppose that CD = AC and that the altitude of the trapezoid is equal to AB. Compute AB/CD.
CD^2 = [ AB + (CD - AB) / 2 ] ^2 + AB^2
CD^2 = [ AB + CD ]^2 / 4 + AB^2
4CD^2 = AB^2 + 2AB *CD + CD^2 + 4AB^2
3CD^2 = 2AB * CD + 5AB^2
3CD^2 -2AB * CD -5 AB^2 = 0
(3CD - 5AB) ( CD + AB) = 0
Either CD = - AB (reject) or
3CD - 5AB = 0
3CD = 5AB
AB / CD = 3 / 5
