Question

find the length x.

Explanation:

Step1: Identify similar triangles

The two triangles are similar by AA similarity (shared angle, right angles).

Step2: Set up proportion

The ratio of corresponding sides is equal: $\frac{x}{2.5} = \frac{10+2}{10}$

Step3: Simplify denominator

$\frac{x}{2.5} = \frac{12}{10}$

Step4: Solve for x

$x = 2.5 \times \frac{12}{10}$
$x = 2.5 \times 1.2$

Answer:

3