Question

A square has side lengths of 14 centimeters. A similar but dilated square has side lengths of 12.25 centimeters. What is the scale factor?(1 point)
Responses

9/4

3/2

4/5

7/8

Answer 1

To find the scale factor between the two squares, we compare the side lengths of the original square and the dilated square.

Given:
- Original square side length = 14 cm
- Dilated square side length = 12.25 cm

The scale factor is calculated as follows:

\[
\text{Scale factor} = \frac{\text{Side length of the dilated square}}{\text{Side length of the original square}} = \frac{12.25}{14}
\]

Now, let's simplify \(\frac{12.25}{14}\):

Convert 12.25 to a fraction:
\[
12.25 = \frac{1225}{100} = \frac{49}{4}
\]

Now calculate the scale factor:
\[
\text{Scale factor} = \frac{49/4}{14} = \frac{49}{4} \div 14 = \frac{49}{4} \times \frac{1}{14} = \frac{49}{56} = \frac{7}{8}
\]

Thus, the scale factor is \( \frac{7}{8} \).

So the correct response is:
**7/8**