Question

the accompanying diagram shows two similar triangles. which proportion could be used to solve for x?
\\( \frac { 12 } { x } = \frac { 32 } { 15 } \\)
\\( \frac { 24 } { 15 } = \frac { x } { 9 } \\)
\\( \frac { x } { 15 } = \frac { 32 } { 12 } \\)
\\( \frac { 24 } { 15 } = \frac { 9 } { x } \\)

Explanation:

Step1: Identify corresponding sides

For similar triangles, the ratios of corresponding sides are equal. Here, the side of length \(24\) in the first triangle corresponds to the side of length \(9\) in the second triangle, and the side of length \(x\) in the first triangle corresponds to the side of length \(15\) in the second triangle.

Step2: Set up the proportion

The proportion should be \(\frac{24}{9}=\frac{x}{15}\) (since the ratio of the longer side to the shorter side in the first triangle should equal the ratio of the longer side to the shorter side in the second triangle).

Answer:

\(\frac{24}{9}=\frac{x}{15}\)