Question

find the length x.

Explanation:

Step1: Use similarity of triangles

The two right - angled triangles are similar. The ratio of their corresponding sides is equal. The ratio of the vertical sides is the same as the ratio of the horizontal sides. The ratio of the vertical sides is $\frac{4}{4 + 6}=\frac{4}{10}=\frac{2}{5}$.

Step2: Set up proportion

Let the length of the unknown side be $x$. We have the proportion $\frac{x}{7.5}=\frac{4}{4 + 6}$. Cross - multiplying gives us $10x=4\times7.5$.

Step3: Solve for $x$

$10x = 30$, so $x=\frac{30}{10}=3$.

Answer:

$3$