Question

polygon i is a scaled copy of polygon h.
what scale factor takes polygon h to polygon i?

Explanation:

Step1: Convert mixed numbers to improper fractions

For \(8\frac{2}{5}\), \(8\frac{2}{5}=\frac{8\times5 + 2}{5}=\frac{42}{5}\). For \(12\frac{3}{5}\), \(12\frac{3}{5}=\frac{12\times5+3}{5}=\frac{63}{5}\).

Step2: Calculate the scale factor

The scale factor \(k\) is the ratio of the corresponding side lengths of the scaled - copy (polygon \(I\)) to the original (polygon \(H\)). Using the vertical sides (we could also use the other pair of corresponding sides), \(k=\frac{12\frac{3}{5}}{8\frac{2}{5}}\). Substituting the improper - fraction forms: \(k = \frac{\frac{63}{5}}{\frac{42}{5}}\). Since \(\frac{a/b}{c/b}=\frac{a}{c}\) (when \(b
eq0\)), then \(k=\frac{63}{42}\). Simplifying \(\frac{63\div21}{42\div21}=\frac{3}{2}=1.5\).

Answer:

\(1.5\)