A triangle has side lengths of 2, 6, and 7 units, and a similar but larger triangle has corresponding side lengths of 6, 18, and 21 units. Calculate and compare the perimeters of the triangles. What is the ratio of the corresponding sides of the smaller triangle to the larger triangle?(1 point)

Question

Responses

3
3

19
Start Fraction 1 over 9 End Fraction

1
1

13
Start Fraction 1 over 3 End Fraction
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Answer 1

To find the perimeters of the triangles and the ratio of the corresponding sides, follow these steps:

1. Calculate the perimeter of the smaller triangle:

   • The side lengths of the smaller triangle are 2, 6, and 7.
   • Perimeter = 2 + 6 + 7 = 15 units.

2. Calculate the perimeter of the larger triangle:

   • The side lengths of the larger triangle are 6, 18, and 21.
   • Perimeter = 6 + 18 + 21 = 45 units.

3. Find the ratio of the corresponding sides of the smaller triangle to the larger triangle:

   • The corresponding sides are 2 (small) to 6 (large), 6 to 18, and 7 to 21.
   • The ratio for each pair is:
     • 2:6 = 2/6 = 1/3
     • 6:18 = 6/18 = 1/3
     • 7:21 = 7/21 = 1/3
   • Thus, the ratio of the sides of the smaller triangle to the larger triangle is consistently 1:3.

4. Summary:

   • The perimeter of the smaller triangle is 15 units.
   • The perimeter of the larger triangle is 45 units.
   • The ratio of the corresponding sides of the smaller triangle to the larger triangle is 1:3.

Therefore, the answer to your question about the ratio of the corresponding sides of the smaller triangle to the larger triangle is Start Fraction 1 over 3 End Fraction.