Question

rectangle y is a scaled copy of rectangle x. what scale factor takes rectangle x to rectangle y? rectangle x: length $3\frac{3}{5}$, width $2\frac{2}{5}$. rectangle y: length $3\frac{3}{20}$, width $2\frac{1}{10}$

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{2}{5}=\frac{2\times5 + 2}{5}=\frac{12}{5}$, $2\frac{1}{10}=\frac{2\times10+1}{10}=\frac{21}{10}$, $3\frac{3}{5}=\frac{3\times5 + 3}{5}=\frac{18}{5}$, $3\frac{3}{20}=\frac{3\times20+3}{20}=\frac{63}{20}$

Step2: Calculate the scale factor using one of the side - length ratios

We can use the ratio of the corresponding side - lengths. Let's use the shorter side - lengths. The scale factor $k$ is given by the ratio of the side - length of rectangle $Y$ to the side - length of rectangle $X$. So $k=\frac{\frac{21}{10}}{\frac{12}{5}}$

Step3: Simplify the fraction

$k=\frac{21}{10}\div\frac{12}{5}=\frac{21}{10}\times\frac{5}{12}=\frac{21\times5}{10\times12}=\frac{105}{120}=\frac{7}{8}$

Answer:

$\frac{7}{8}$