Question

the two right triangles below are similar. which equation could you sol to find this triangle?
\\( \frac { x } { 13 } = \frac { 5 } { 12 } \\)
\\( \frac { 13 } { 12 } = \frac { 9 } { x } \\)
\\( \frac { 12 } { 13 } = \frac { 9 } { x } \\)

Explanation:

Step1: Recall the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

In the two right - angled triangles, the side of length \(12\) in the larger triangle corresponds to the side of length \(9\) in the smaller triangle, and the side of length \(13\) in the larger triangle corresponds to the hypotenuse \(x\) of the smaller triangle.
So, the proportion is \(\frac{12}{13}=\frac{9}{x}\)

Answer:

\(\frac{12}{13}=\frac{9}{x}\)