Question

multiple choice 4 points
the accompanying diagram shows two similar triangles.
which proportion could be used to solve for x?
$\frac{12}{x}=\frac{32}{15}$
$\frac{24}{15}=\frac{x}{9}$
$\frac{x}{15}=\frac{32}{12}$
$\frac{9}{x}=\frac{24}{15}$

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 similar triangles, \(9\) corresponds to \(24\), \(15\) corresponds to \(x\), and \(12\) corresponds to \(32\). The ratio of the first pair of corresponding sides (\(9\) and \(24\)) should be equal to the ratio of the second pair of corresponding sides (\(15\) and \(x\)). So the proportion is \(\frac{9}{24}=\frac{15}{x}\), which can be rewritten as \(\frac{24}{9}=\frac{x}{15}\) (by cross - multiplying and re - arranging).

Answer:

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