Question

polygon d is a scaled copy of polygon c.
polygon c (with side lengths 2, 2, 1.6) and polygon d (with side lengths 1.5, 1.5, 1.2) are shown.
what scale factor takes polygon c to polygon d?
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solve one-step multiplication and division equations with decimals
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Explanation:

Step1: Recall scale factor formula

The scale factor from polygon \( C \) to polygon \( D \) is the ratio of a corresponding side length of \( D \) to the corresponding side length of \( C \). Let's take the side with length \( 2 \) in \( C \) and \( 1.5 \) in \( D \), or the side with length \( 1.6 \) in \( C \) and \( 1.2 \) in \( D \). We'll use the first pair: \( \text{Scale Factor} = \frac{\text{Length in } D}{\text{Length in } C} \)

Step2: Calculate using side lengths

Using the side of length \( 2 \) in \( C \) and \( 1.5 \) in \( D \): \( \frac{1.5}{2} = 0.75 \). We can verify with the other pair: \( \frac{1.2}{1.6} = 0.75 \) (since \( 1.2\div1.6 = \frac{12}{16}=\frac{3}{4}=0.75 \)).

Answer:

\( 0.75 \) (or \( \frac{3}{4} \))