Question

find the length x.

Explanation:

Step1: Use similar - triangles property

The two right - angled triangles are similar. The ratio of the corresponding sides of similar triangles is equal. The ratio of the vertical sides of the two similar triangles is $\frac{6}{6 + 3}=\frac{6}{9}=\frac{2}{3}$. The ratio of the horizontal sides should be the same.

Step2: Set up the proportion

Let the length of the unknown side be $x$. We have the proportion $\frac{x}{6}=\frac{6}{6 + 3}$.

Step3: Solve the proportion for $x$

Cross - multiply: $9x=6\times6$. Then $9x = 36$. Divide both sides by 9: $x=\frac{36}{9}=4$.

Answer:

$4$