Question

find the length x.

Explanation:

Step1: Use similar - triangle property

Since the two right - angled triangles are similar, the ratios of their corresponding sides are equal.
Let the two similar right - angled triangles have side - length ratios. The ratio of the hypotenuses is the same as the ratio of the horizontal sides.
We have the proportion $\frac{4.5}{4.5 + 4.5}=\frac{3.5}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{4.5}{9}=\frac{3.5}{x}$ gives us $4.5x=3.5\times9$.

Step3: Solve for $x$

First, calculate $3.5\times9 = 31.5$. Then, $x=\frac{31.5}{4.5}=7$.

Answer:

$7$