Question

find the length x.

Explanation:

Step1: Use similar - triangles property

The two right - angled triangles are similar. The ratio of their corresponding sides is equal. The ratio of the vertical sides of the two similar triangles is $\frac{6}{6 + 4.5}=\frac{6}{10.5}=\frac{4}{7}$. Since the triangles are similar, the ratio of the horizontal sides is the same.

Step2: Set up proportion equation

We have the proportion $\frac{4}{x}=\frac{6}{6 + 4.5}$. Cross - multiply to get $6x=4\times(6 + 4.5)$.

Step3: Solve for $x$

First, calculate $4\times(6 + 4.5)=4\times10.5 = 42$. Then, $x=\frac{42}{6}=7$.

Answer:

$7$