Question

given the triangles are similar, which equation would correctly solve for x?
\\( \frac { 5 } { 4 } = \frac { x } { 8 } \\)
\\( \frac { 4 } { 5 } = \frac { x } { 8 } \\)
\\( \frac { 5 } { 4 } = \frac { 8 } { x } \\)

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. Let's assume the sides of the smaller triangle are \(4\) and \(5\), and the corresponding sides of the larger triangle are \(8\) and \(x\).

Step2: Set up the proportion

The proportion should be \(\frac{5}{4}=\frac{x}{8}\) (since the ratio of the longer side to the shorter side in the smaller triangle is equal to the ratio of the longer side to the shorter side in the larger triangle).

Answer:

\(\frac{5}{4}=\frac{x}{8}\)