find the value of x using the figure to the right.\nx = \\square (simplify your answer.)

Explanation:

Step1: Identify similar triangles

The large right triangle and the smaller right triangle (with side $x$) are similar, so corresponding sides are proportional.

Step2: Set up proportion

$\frac{x}{8} = \frac{8}{12}$

Step3: Solve for $x$

$x = 8 \times \frac{8}{12} = \frac{64}{12} = \frac{16}{3}$

Answer:

$\frac{16}{3}$