Certainly! Let's solve this problem step-by-step.
1. Identify the given information:
- We are given that triangle [tex]\( A \)[/tex] was enlarged proportionally.
- Each side of triangle [tex]\( A \)[/tex] was made 2.5 times as long to form triangle [tex]\( B \)[/tex].
- The shortest side in triangle [tex]\( A \)[/tex] measures 25 units.
2. Use the proportion to find the length of the shortest side in triangle [tex]\( B \)[/tex]:
Since each side of triangle [tex]\( A \)[/tex] is enlarged by a factor of 2.5 to form triangle [tex]\( B \)[/tex]:
[tex]\[
\text{Shortest side in triangle } B = \text{Shortest side in triangle } A \times 2.5
\][/tex]
[tex]\[
\text{Shortest side in triangle } B = 25 \times 2.5
\][/tex]
So, the shortest side in triangle [tex]\( B \)[/tex] measures 62.5 units.
3. Ratio of lengths:
The ratio of a length in triangle [tex]\( B \)[/tex] to the corresponding length in triangle [tex]\( A \)[/tex] is given by the scale factor used in the enlargement:
[tex]\[
\text{Ratio} = 2.5
\][/tex]
So, we can complete the statements as follows:
- The shortest side in triangle [tex]\( B \)[/tex] has a measure of 62.5 units.
- The ratio of a length in triangle [tex]\( B \)[/tex] to the corresponding length in triangle [tex]\( A \)[/tex] is equal to 2.5.
Simple as that!
