To determine if one triangle is a dilation of the other, we need to verify whether the corresponding sides of the two triangles have the same ratio. Here, the sets of ratios under consideration are:
[tex]\[
\frac{3.6}{3}, \quad \frac{5.4}{4.5}, \quad \text{and} \quad \frac{6}{5}
\][/tex]
We need to calculate each of these ratios and then compare them to see if they are equal.
1. Calculating the first ratio:
[tex]\[
\frac{3.6}{3} = 1.2
\][/tex]
2. Calculating the second ratio:
[tex]\[
\frac{5.4}{4.5} \approx 1.2000000000000002
\][/tex]
3. Calculating the third ratio:
[tex]\[
\frac{6}{5} = 1.2
\][/tex]
Next, we compare these calculated ratios to determine if they are all equal:
- The first ratio is [tex]\(1.2\)[/tex]
- The second ratio is approximately [tex]\(1.2000000000000002\)[/tex]
- The third ratio is [tex]\(1.2\)[/tex]
Although [tex]\(1.2000000000000002\)[/tex] is extremely close to [tex]\(1.2\)[/tex], they are not exactly the same due to minor floating-point arithmetic inconsistencies.
Therefore, since the calculated ratios are not exactly equal, the set of ratios [tex]\(\frac{3.6}{3} = \frac{5.4}{4.5} = \frac{6}{5}\)[/tex] cannot strictly be used to determine if one triangle is a dilation of the other. Thus, the final answer is that these ratios indicate the triangles are not guaranteed to be dilations of each other.
