Question

Find the value of x.

Answer 1

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.

$\frac{12}{x}=\frac{x}{16}$

This gives us, by cross multiplication,

$x^2=12(16)$ and

$x^2=192$ so

x = $\sqrt{192}$ or $8\sqrt{3}$