Question

Find the scale factor. Triangle ABC lines AB(16)BC(14)AC(12). Triangle TVU lines TV(21)VU(24)(TU(18)

Answer 1

To find the scale factor between the two triangles, we need to compare the lengths of their corresponding sides.

For Triangle ABC:
- AB = 16
- BC = 14
- AC = 12

For Triangle TVU:
- TV = 21
- VU = 24
- TU = 18

Now we can find the scale factor by comparing each corresponding side:

1. For sides AB and TV:
\[
\text{Scale factor} = \frac{TV}{AB} = \frac{21}{16}
\]

2. For sides BC and VU:
\[
\text{Scale factor} = \frac{VU}{BC} = \frac{24}{14} = \frac{12}{7}
\]

3. For sides AC and TU:
\[
\text{Scale factor} = \frac{TU}{AC} = \frac{18}{12} = \frac{3}{2}
\]

Now, we should check if the scale factors are consistent for all corresponding sides to determine if the triangles are similar. However, in this case, the scale factors calculated are different:
- From AB to TV: \(\frac{21}{16}\)
- From BC to VU: \(\frac{12}{7}\)
- From AC to TU: \(\frac{3}{2}\)

Since the scale factors are not equal, the triangles ABC and TVU are not similar, so there is no single scale factor that applies to both triangles.