Question

pentagon m is a scaled copy of pentagon l. what is the value of n?

Explanation:

Step1: Convert mixed numbers to improper fractions

Convert \(1\frac{1}{2}\) to \(\frac{3}{2}\), \(1\frac{1}{8}\) to \(\frac{9}{8}\).

Step2: Find the scale factor

The scale factor \(k\) is \(\frac{\text{corresponding side of }M}{\text{corresponding side of }L}\), so \(k=\frac{\frac{9}{8}}{\frac{3}{2}}=\frac{9}{8}\times\frac{2}{3}=\frac{3}{4}\).

Step3: Calculate \(n\)

Since \(n = 5\times k\), substitute \(k = \frac{3}{4}\), then \(n=5\times\frac{3}{4}=\frac{15}{4}=3\frac{3}{4}\).

Answer:

\(3\frac{3}{4}\)