EXPLANATION
We can apply the Triangle Similarity Theorem in order to get the value of x as shown as follows:
[tex]\frac{\text{Hypotenuse}_{\text{outer}}}{\text{Hypotenuse\_inner}}=\frac{\text{adjacent outer}}{\text{adjacent inner}}[/tex]
Replacing terms:
[tex]\frac{27}{12}=\frac{12}{x}[/tex]
Reversing the fractions:
[tex]\frac{12}{27}=\frac{x}{12}[/tex]
Multiplying both sides by 12:
[tex]\frac{12\cdot12}{27}=x[/tex]
Multiplying numbers and simplifying:
[tex]\frac{16}{3}=x[/tex]
The answer is the option D: 16/3