Question

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)
Responses

13
Start Fraction 1 over 3 End Fraction

3
3

19
Start Fraction 1 over 9 End Fraction

1
1

Answer 1

To calculate the perimeters of the triangles, we first find the perimeter of each triangle by summing the lengths of their sides.

For the smaller triangle with side lengths of 2, 6, and 7:

\[
\text{Perimeter of smaller triangle} = 2 + 6 + 7 = 15 \text{ units}
\]

For the larger triangle with corresponding side lengths of 6, 18, and 21:

\[
\text{Perimeter of larger triangle} = 6 + 18 + 21 = 45 \text{ units}
\]

Now we can compare the perimeters:

- Perimeter of the smaller triangle: \(15\) units
- Perimeter of the larger triangle: \(45\) units

Next, we find the ratio of the corresponding sides of the smaller triangle to the larger triangle. To do this, we take any corresponding side lengths from each triangle:

For example, using the first side:
- Smaller triangle side: \(2\) units
- Larger triangle side: \(6\) units

The ratio is:

\[
\frac{\text{Smaller side}}{\text{Larger side}} = \frac{2}{6} = \frac{1}{3}
\]

So, the ratio of any corresponding side of the smaller triangle to the larger triangle is \( \frac{1}{3} \).

Therefore, the perimeters calculated are:

- Smaller triangle: \(15\) units
- Larger triangle: \(45\) units

And the ratio of the corresponding sides of the smaller triangle to the larger triangle is \( \frac{1}{3} \).

The correct response is:
**Start Fraction 1 over 3 End Fraction**.