Question

polygon i is a scaled copy of polygon ii.
image: polygon h (blue) with sides labeled ( 4 \frac{4}{9} ), ( 6 \frac{4}{9} ), ( 8 \frac{2}{9} ); polygon i (green) with sides labeled ( 7 \frac{1}{3} ), ( 10 \frac{1}{3} ), ( 12 \frac{3}{5} ) (or similar)
what scale factor takes polygon h to polygon i?

Explanation:

Step1: Convert mixed numbers to improper fractions

For Polygon H's side \(4\frac{4}{5}\), convert to improper fraction: \(4\frac{4}{5}=\frac{4\times5 + 4}{5}=\frac{24}{5}\)
For Polygon I's corresponding side \(7\frac{1}{5}\), convert to improper fraction: \(7\frac{1}{5}=\frac{7\times5+1}{5}=\frac{36}{5}\)

Step2: Calculate the scale factor

Scale factor is the ratio of the length of the side in Polygon I to the length of the corresponding side in Polygon H. So, scale factor \(=\frac{\frac{36}{5}}{\frac{24}{5}}\)
When dividing fractions, we multiply by the reciprocal: \(\frac{36}{5}\times\frac{5}{24}=\frac{36}{24}\)
Simplify \(\frac{36}{24}\) by dividing numerator and denominator by 12: \(\frac{36\div12}{24\div12}=\frac{3}{2}=1\frac{1}{2}\)

We can also check with another pair of sides. For example, Polygon H's side \(8\frac{2}{5}=\frac{8\times5 + 2}{5}=\frac{42}{5}\), Polygon I's corresponding side \(12\frac{3}{5}=\frac{12\times5+3}{5}=\frac{63}{5}\). Then \(\frac{\frac{63}{5}}{\frac{42}{5}}=\frac{63}{42}=\frac{3}{2}\), which confirms the scale factor.

Answer:

\(\frac{3}{2}\) (or \(1\frac{1}{2}\))