Question

parallelogram c is a scaled copy of parallelogram b. what scale factor takes parallelogram b to parallelogram c?

Explanation:

Step1: Convert mixed numbers to improper fractions

$35=\frac{35}{1}$, $24\frac{1}{2}=\frac{24\times2 + 1}{2}=\frac{49}{2}$, $12\frac{1}{2}=\frac{12\times2+1}{2}=\frac{25}{2}$, $8\frac{3}{4}=\frac{8\times4 + 3}{4}=\frac{35}{4}$

Step2: Find the scale factor using the ratio of corresponding sides

We can use the ratio of the longer sides (or the shorter sides). Let's use the longer sides.
The scale factor $k=\frac{\text{length of side in C}}{\text{length of side in B}}$
Using the longer sides: $k=\frac{24\frac{1}{2}}{35}=\frac{\frac{49}{2}}{35}=\frac{49}{2}\times\frac{1}{35}=\frac{49}{70}=\frac{7}{10}$
We can check with the shorter sides: $\frac{8\frac{3}{4}}{12\frac{1}{2}}=\frac{\frac{35}{4}}{\frac{25}{2}}=\frac{35}{4}\times\frac{2}{25}=\frac{70}{100}=\frac{7}{10}$

Answer:

$\frac{7}{10}$