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Answer :
To determine if one triangle is a dilation of another, we need to check if their side lengths are proportional. The side lengths of two triangles are proportional if the ratios of corresponding sides are equal.
Let's examine the given ratios:
1. [tex]\(\frac{3.8}{3}\)[/tex]
2. [tex]\(\frac{54}{4.5}\)[/tex]
3. [tex]\(\frac{8}{6}\)[/tex]
We need to compare these ratios to see if any of them are equal:
1. Calculate the first ratio, [tex]\(\frac{3.8}{3}\)[/tex]:
- This ratio simplifies to approximately 1.2667.
2. Calculate the second ratio, [tex]\(\frac{54}{4.5}\)[/tex]:
- This ratio simplifies to 12.0.
3. Calculate the third ratio, [tex]\(\frac{8}{6}\)[/tex]:
- This ratio simplifies to approximately 1.3333.
Next, we compare these simplified ratios to see if any of them are equivalent, which would indicate proportional sides:
- Compare [tex]\(\frac{3.8}{3}\)[/tex] and [tex]\(\frac{54}{4.5}\)[/tex] (1.2667 vs. 12.0): These are not equal.
- Compare [tex]\(\frac{3.8}{3}\)[/tex] and [tex]\(\frac{8}{6}\)[/tex] (1.2667 vs. 1.3333): These are not equal.
- Compare [tex]\(\frac{54}{4.5}\)[/tex] and [tex]\(\frac{8}{6}\)[/tex] (12.0 vs. 1.3333): These are not equal.
Since none of the ratios are equal, no set of these ratios can be used to confirm that one triangle is a dilation of another. Therefore, the given ratios do not represent proportional side lengths of two triangles, and thus cannot determine if one is a dilation of the other.
Let's examine the given ratios:
1. [tex]\(\frac{3.8}{3}\)[/tex]
2. [tex]\(\frac{54}{4.5}\)[/tex]
3. [tex]\(\frac{8}{6}\)[/tex]
We need to compare these ratios to see if any of them are equal:
1. Calculate the first ratio, [tex]\(\frac{3.8}{3}\)[/tex]:
- This ratio simplifies to approximately 1.2667.
2. Calculate the second ratio, [tex]\(\frac{54}{4.5}\)[/tex]:
- This ratio simplifies to 12.0.
3. Calculate the third ratio, [tex]\(\frac{8}{6}\)[/tex]:
- This ratio simplifies to approximately 1.3333.
Next, we compare these simplified ratios to see if any of them are equivalent, which would indicate proportional sides:
- Compare [tex]\(\frac{3.8}{3}\)[/tex] and [tex]\(\frac{54}{4.5}\)[/tex] (1.2667 vs. 12.0): These are not equal.
- Compare [tex]\(\frac{3.8}{3}\)[/tex] and [tex]\(\frac{8}{6}\)[/tex] (1.2667 vs. 1.3333): These are not equal.
- Compare [tex]\(\frac{54}{4.5}\)[/tex] and [tex]\(\frac{8}{6}\)[/tex] (12.0 vs. 1.3333): These are not equal.
Since none of the ratios are equal, no set of these ratios can be used to confirm that one triangle is a dilation of another. Therefore, the given ratios do not represent proportional side lengths of two triangles, and thus cannot determine if one is a dilation of the other.
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