find the value of x by using the Geometric Mean (Altitude) Theorem.

Step-by-step solution-:

By using the Geometric Mean (Altitude) Theorem:

(CD)^2=AD\times{DB}

Substitute the CD=12, AD=x, and DB=16 into the Geometric Mean (Altitude) Theorem:

\textcolor{primary}{12^{2}}=\textcolor{secondary}{x}\cdot \textcolor{tertiary}{16}\implies144=16x

After solving:

16x=144\implies x=\frac{\cancel{144}}{\cancel{16}}=9

The value of x is 9:

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