Question

quadrilateral e is a scaled copy of quadrilateral d.
image of quadrilateral d (with side lengths 12 and 8) and quadrilateral e (with side lengths $8\frac{2}{5}$ and $5\frac{3}{5}$)
what scale factor takes quadrilateral d to quadrilateral e?

Explanation:

Step1: Convert mixed numbers to improper fractions

For the side of Quadrilateral E with length \( 5\frac{3}{5} \), we convert it to an improper fraction: \( 5\frac{3}{5}=\frac{5\times5 + 3}{5}=\frac{28}{5} \).
For the corresponding side of Quadrilateral D with length 8, we can write it as \( \frac{40}{5} \).
For the other pair of sides, Quadrilateral E has \( 8\frac{2}{5}=\frac{8\times5+2}{5}=\frac{42}{5} \) and Quadrilateral D has 12, which is \( \frac{60}{5} \).

Step2: Calculate the scale factor

The scale factor is the ratio of the length of a side in E to the corresponding side in D. Let's use the first pair of sides (length 8 in D and \( 5\frac{3}{5} \) in E).
Scale factor \( k=\frac{\text{Length in E}}{\text{Length in D}}=\frac{\frac{28}{5}}{8}=\frac{28}{5}\div8=\frac{28}{5}\times\frac{1}{8}=\frac{28}{40}=\frac{7}{10} \).
We can verify with the other pair: \( \frac{\frac{42}{5}}{12}=\frac{42}{5}\div12=\frac{42}{5}\times\frac{1}{12}=\frac{42}{60}=\frac{7}{10} \).

Answer:

\( \frac{7}{10} \)