Question

the given figures are similar. write a proportion for the following and solve for n. * both \\( \delta \\)s are not right triangles. \\( \triangle g h i \sim \triangle p q r \\) proportion \\( \
ightarrow \frac{3}{n}=\frac{7}{16} \\) \\( n= \\)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{3}{n}=\frac{7}{16}\), cross - multiplying gives \(7n = 3\times16\).

Step2: Simplify the right - hand side

Calculate \(3\times16 = 48\), so the equation becomes \(7n=48\).

Step3: Solve for \(n\)

Divide both sides of the equation \(7n = 48\) by \(7\), we get \(n=\frac{48}{7}\approx6.86\).

Answer:

\(n=\frac{48}{7}\)