Answer:
Step-by-step explanation:
To solve for x, you need the formula for the geometric means for similar right triangles. The big triangle is a right triangle; therefore, it is similar by definition, to the other right triangle. The 2 right triangles have the same hypotenuse, x. So we use the hypotenuse to find the value of x.
[tex]\frac{12}{x}=\frac{x}{16}[/tex]
This gives us, by cross multiplication,
[tex]x^2=12(16)[/tex] and
[tex]x^2=192[/tex] so
x = [tex]\sqrt{192}[/tex] or [tex]8\sqrt{3}[/tex]
