Question

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

Explanation:

Step1: Convert mixed numbers to improper fractions

$3\frac{1}{3}=\frac{3\times3 + 1}{3}=\frac{10}{3}$, $2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$, $1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2}$, $1\frac{1}{8}=\frac{1\times8+1}{8}=\frac{9}{8}$

Step2: Find the scale factor

The scale factor $k$ is the ratio of corresponding sides. Using the top - side lengths: $k=\frac{\frac{9}{8}}{\frac{3}{2}}=\frac{9}{8}\times\frac{2}{3}=\frac{3}{4}$

Step3: Calculate the value of $n$

Since $n$ corresponds to the side of length $5$ in pentagon $L$, we use the formula $n = 5\times k$. Substitute $k=\frac{3}{4}$ into the formula: $n = 5\times\frac{3}{4}=\frac{15}{4}=3\frac{3}{4}$

Answer:

$3\frac{3}{4}$