Question

a regular octagon is an eight-sided polygon with side lengths that are all equal. all three octagons are scale drawings of each other. use the chart and the side lengths to compute each scale factor as a percent. how can we check our answers?drawing 1 (side length 10)drawing 2 (side length 12)drawing 3 (side length 8)| actual drawing to scale drawing | scale factor | equation to illustrate relationship || ---- | ---- | ---- || drawing 1 to drawing 2 | $\frac{12}{10}=1.2$ $\frac{1.2}{100}=120%$ | || drawing 1 to drawing 3 | | || drawing 2 to drawing 1 | | |

Explanation:

Step1: Find scale factor (Drawing1→3)

Divide target side by original side, convert to percent.
$\frac{8}{10}=0.8 = 80\%$
Equation: $10 \times 0.8 = 8$

Step2: Find scale factor (Drawing2→1)

Divide target side by original side, convert to percent.
$\frac{10}{12} \approx 0.833 = 83.3\%$
Equation: $12 \times \frac{10}{12} = 10$

Step3: Explain checking method

Verify by reversing scale factors, or multiply original side by scale factor to match target side.

Answer:

Actual Drawing to Scale Drawing	Scale Factor	Equation to Illustrate Relationship
Drawing 1 to Drawing 3	80%	$10 \times 0.8 = 8$
Drawing 2 to Drawing 1	$\approx83.3\%$	$12 \times \frac{10}{12} = 10$

To check answers:

1. Reverse the scale factor calculation (e.g., use the scale factor from Drawing 2 to 1 on Drawing 1's side length to see if you get Drawing 2's side length).
2. Multiply the original figure's side length by the calculated scale factor and confirm it equals the target figure's side length.