9514 1404 393
Answer:
x = √66
Explanation:
In a geometry like this, the right triangles are all similar. Then the length of the long side to the hypotenuse is ...
6/x = x/(6+5)
6·11 = x²
x = √66
_____
Additional comment
The relation g=√(ab) gives the geometric mean (g) of the two numbers 'a' and 'b'. In this geometry, there are three geometric mean relationships.
long side = geometric mean(long segment, hypotenuse) . . . x = √(6·11)
short side = geometric mean(short segment, hypotenuse) . . . y = √(5·11)
altitude = geometric mean(long segment, short segment) . . . BD = √(6·5)