When we have a right triangle like this...we have the following relationship
12/ height = height/ 9 cross-multiply
108 = height^2 take the positive root
√108 = height
Using the Pythagorean Theorem.....
y = √ [ (√108)^2 + 12^2 ]
y = √ [ 108 + 144]
y = √252 = √ { 7 * 36 ] = 6 √ 7