To determine if one triangle is a dilation of another, we need to check if the ratios of corresponding sides are equal. For two triangles to be related by dilation, each pair of corresponding sides must maintain the same ratio.
Let's break down and evaluate each ratio provided:
1. Evaluate the first ratio:
[tex]\[
\frac{3.6}{3}
\][/tex]
Simplifies to:
[tex]\[
\frac{3.6}{3} = 1.2
\][/tex]
2. Evaluate the second ratio:
[tex]\[
\frac{5.4}{4.5}
\][/tex]
Simplifies to:
[tex]\[
\frac{5.4}{4.5} = 1.2
\][/tex]
3. Evaluate the third ratio:
[tex]\[
\frac{6}{5}
\][/tex]
Simplifies to:
[tex]\[
\frac{6}{5} = 1.2
\][/tex]
Now, let's examine these results:
- The first ratio is [tex]\( 1.2 \)[/tex].
- The second ratio is [tex]\( 1.2000000000000002 \)[/tex].
- The third ratio is [tex]\( 1.2 \)[/tex].
Though they seem to be very close and practically identical, for strict mathematical equality, they must be exactly the same.
Since there is a minor difference in the second ratio (1.2000000000000002 instead of 1.2), these ratios are not perfectly equal. Thus, strictly speaking, these numbers suggest that the triangles are not a perfect dilation because the ratios are not exactly the same.
In conclusion, given these ratios:
[tex]\(\frac{3.6}{3}\)[/tex], [tex]\(\frac{5.4}{4.5}\)[/tex], and [tex]\(\frac{6}{5}\)[/tex], we find that they are nearly equal but not exactly equal. Hence, one triangle is not a perfect dilation of the other.
