Question

The two triangles below are similar. Which pair are corresponding sides?

Triangle L M N. Side L M is 7, M N is 5, L N is 4. Triangle P Q R. Side P Q is 8.8, Q R is 11, R P is 15.4.
LN and MN
MN and RQ
LM and QR
LM and PQ

Answer 1

To determine the corresponding sides of the two similar triangles, we can use the ratios of the lengths of the sides.

For Triangle LMN:
- LM = 7
- MN = 5
- LN = 4

For Triangle PQR:
- PQ = 8.8
- QR = 11
- RP = 15.4

To find the corresponding sides, we can calculate the ratios between the sides of the two triangles:

1. Calculate the ratios for each pair of sides:
- LM and PQ: \( \frac{LM}{PQ} = \frac{7}{8.8} \)
- MN and QR: \( \frac{MN}{QR} = \frac{5}{11} \)
- LN and RP: \( \frac{LN}{RP} = \frac{4}{15.4} \)

Now, we calculate those ratios to see if they are equal:

1. \( \frac{7}{8.8} = 0.79545 \)
2. \( \frac{5}{11} = 0.45454 \)
3. \( \frac{4}{15.4} = 0.25974 \)

Next, we will also find the pairs of corresponding sides:
- Comparing LM and PQ: The ratio \( \frac{LM}{PQ} \) does not match with the other ratios indicating they are not corresponding.
- Comparing MN and QR: The ratio \( \frac{MN}{QR} \) does not match.
- Comparing LN and RP: The ratio \( \frac{LN}{RP} \) does not match.

After checking the possible options (LN and MN, MN and QR, LM and QR, LM and PQ), the corresponding sides based on the order of triangles would be:

- LM corresponds to PQ
- MN corresponds to QR
- LN corresponds to RP

Thus, the only pair of corresponding sides that matches the ratios is:
**LM and PQ**

Therefore, the corresponding sides are:
- **LM and PQ**.