Question

find the length x.

Explanation:

Step1: Use similar - triangle property

Since the two right - triangles are similar, the ratios of their corresponding sides are equal. The ratio of the short sides of the two similar triangles is the same as the ratio of the long sides.
Let the two similar right - triangles have side lengths such that $\frac{4.5}{x}=\frac{6}{6 + 6}$.

Step2: Cross - multiply and solve for x

Cross - multiplying gives $6x=4.5\times(6 + 6)$.
First, calculate $4.5\times(6 + 6)=4.5\times12 = 54$.
Then, solve for $x$ from $6x = 54$, so $x=\frac{54}{6}=9$.

Answer:

9