Use the geometric mean for right triangles as the sides are related to the hypotenuse. 30 - 6 = 24. We need that for our proportion. [tex] \frac{24}{x}=\frac{x}{30} [/tex]. We cross-multiply to get [tex] x^2=720 [/tex]. Taking the square root of both sides gives us that [tex] x=12\sqrt{5} [/tex], the second choice above.
