find the length $x$.

Explanation:

Step1: Identify similar triangles

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

Step2: Set up proportion

Corresponding sides are proportional: $\frac{x}{2.5 + x} = \frac{2}{4}$

Step3: Simplify and solve for x

Simplify $\frac{2}{4}=\frac{1}{2}$, so $2x = 2.5 + x$ Subtract $x$ from both sides: $2x - x = 2.5$

Answer:

$5$