Question

find the length x.

Explanation:

Step1: Use similar - triangle property

The two right - triangles are similar. For similar triangles, the ratios of corresponding sides are equal. The ratio of the vertical sides is the same as the ratio of the horizontal sides.
Let the two similar right - triangles have horizontal sides \(a = 4.5\) and \(a + b=4.5 + 4.5=9\), and vertical sides \(c = 2\) and \(d=x\). Then \(\frac{c}{a}=\frac{d}{a + b}\).

Step2: Substitute values and solve for \(x\)

Substitute \(a = 4.5\), \(a + b=9\), and \(c = 2\) into \(\frac{c}{a}=\frac{d}{a + b}\). We get \(\frac{2}{4.5}=\frac{x}{9}\).
Cross - multiply: \(4.5x=2\times9\).
\(4.5x = 18\).
Divide both sides by \(4.5\): \(x=\frac{18}{4.5}=4\).

Answer:

\(4\)