Question

find the length x.

Explanation:

Step1: Use similar - triangles property

The two right - angled triangles are similar. The ratio of corresponding sides of similar triangles is equal.
Let the larger triangle have sides 6 + 6 and 5, and the smaller triangle have sides 6 and x. Then, by the property of similar triangles, we have the proportion $\frac{x}{5}=\frac{6}{6 + 6}$.

Step2: Solve the proportion for x

Cross - multiply the proportion $\frac{x}{5}=\frac{6}{12}$ to get $12x=5\times6$.
Simplify the right - hand side: $12x = 30$.
Divide both sides by 12: $x=\frac{30}{12}=\frac{5}{2}=2.5$.

Answer:

$2.5$