This can be solved by using the geometric mean theorem. The altitude drawn to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse. The geometric mean is numbers for which this statement is true: a/x = x/b where a and b represent 2 numbers. So filling in a/x = x/b with the given information gives you 36/x = x/9. You can then solve by using the means-extremes property. x^2 = 324
x = 18