To solve the problem, we first calculate the perimeters of both triangles and then find the ratio of the corresponding sides.
Step 1: Calculate the perimeter of the smaller triangle.
The side lengths of the smaller triangle are 2, 6, and 7 units.
\[ \text{Perimeter of the smaller triangle} = 2 + 6 + 7 = 15 \text{ units} \]
Step 2: Calculate the perimeter of the larger triangle.
The side lengths of the larger triangle are 6, 18, and 21 units.
\[ \text{Perimeter of the larger triangle} = 6 + 18 + 21 = 45 \text{ units} \]
Step 3: Compare the perimeters of the two triangles.
The perimeter of the smaller triangle is 15 units, while the perimeter of the larger triangle is 45 units.
Step 4: Calculate the ratio of corresponding sides of the smaller triangle to the larger triangle.
The corresponding sides are:
- 2 (smaller) to 6 (larger)
- 6 (smaller) to 18 (larger)
- 7 (smaller) to 21 (larger)
Calculating the ratio for one pair of corresponding sides:
\[ \frac{2}{6} = \frac{1}{3} \]
Calculating the ratio for another pair:
\[ \frac{6}{18} = \frac{1}{3} \]
Calculating for the third pair:
\[ \frac{7}{21} = \frac{1}{3} \]
In all cases, the ratio of the corresponding sides of the smaller triangle to the larger triangle is \(\frac{1}{3}\).
Final Answers:
- Perimeter of smaller triangle: 15 units
- Perimeter of larger triangle: 45 units
- Ratio of corresponding sides of the smaller triangle to the larger triangle: \(\frac{1}{3}\)
Therefore, the correct response from the options you provided is:
Start Fraction 1 over 3 End Fraction