Can anyone help please!?

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  x = √66

Step-by-step 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)

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: