Question

the rectangle on the right is a scaled copy of the rectangle on the left. identify the scale factor. express your answer as a whole number or fraction in simplest form.

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from the left - rectangle to the right - rectangle is given by the ratio of corresponding side lengths. We can use either the ratio of the lengths or the ratio of the widths. Let's use the lengths. If the length of the left rectangle is $l_1$ and the length of the right rectangle is $l_2$, then $k=\frac{l_2}{l_1}$.

Step2: Identify the lengths

Here, $l_1 = 14$ and $l_2=21$.

Step3: Calculate the scale factor

$k=\frac{21}{14}=\frac{3}{2}$

We can also check with the widths. Let the width of the left rectangle be $w_1 = 6$ and the width of the right rectangle be $w_2 = 9$. Then $k=\frac{w_2}{w_1}=\frac{9}{6}=\frac{3}{2}$

Answer:

$\frac{3}{2}$