Question

find the value of x.
x = \square
(simplify your answer.)

Explanation:

Step1: Identify segment ratio

The segments divide the sides proportionally. First, find the ratio of the upper segment to the full side:
$\frac{8+4}{8+4+12} = \frac{12}{24} = \frac{1}{2}$

Step2: Apply triangle proportionality theorem

Set up the proportion for side $x$ and the base side:
$\frac{x}{23} = \frac{8+4}{8+4+12}$
Substitute the ratio from Step1:
$\frac{x}{23} = \frac{1}{2}$
Solve for $x$:
$x = 23 \times \frac{1}{2}$

Answer:

$\frac{23}{2}$