Question

quadrilateral g is a scaled copy of quadrilateral f. what scale factor takes quadrilateral f to quadrilateral g?

Explanation:

Step1: Convert mixed numbers to improper fractions

$5\frac{3}{5}=\frac{5\times5 + 3}{5}=\frac{28}{5}$, $4\frac{4}{5}=\frac{4\times5+4}{5}=\frac{24}{5}$, $4\frac{1}{5}=\frac{4\times5 + 1}{5}=\frac{21}{5}$, $3\frac{3}{5}=\frac{3\times5+3}{5}=\frac{18}{5}$, $14=\frac{14}{1}$, $10\frac{1}{2}=\frac{10\times2 + 1}{2}=\frac{21}{2}$

Step2: Calculate the scale factor using corresponding sides

We can use the pair of sides $14$ (from quadrilateral $F$) and $10\frac{1}{2}$ (from quadrilateral $G$). The scale factor $k$ is given by the formula $k=\frac{\text{length in }G}{\text{length in }F}$.
$k=\frac{10\frac{1}{2}}{14}=\frac{\frac{21}{2}}{14}=\frac{21}{2}\times\frac{1}{14}=\frac{21}{28}=\frac{3}{4}$

We can also check with another pair of sides. For example, using $5\frac{3}{5}=\frac{28}{5}$ (from $F$) and $4\frac{1}{5}=\frac{21}{5}$ (from $G$)
$k = \frac{4\frac{1}{5}}{5\frac{3}{5}}=\frac{\frac{21}{5}}{\frac{28}{5}}=\frac{21}{28}=\frac{3}{4}$

Answer:

$\frac{3}{4}$