Question

Sides of Similar Figures Practice
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Question
Two triangles used in an art project are similar. The sides of the smaller triangle have lengths of 6 in., 7 in., and 12 in. The perimeter of the larger triangle is 75 in. What is the length of the shortest side of the larger triangle?(1 point)
in.

Answer 1

To solve for the length of the shortest side of the larger triangle, we need to determine the scale factor between the smaller and larger triangles.

First, we calculate the perimeter of the smaller triangle:

\[
\text{Perimeter of smaller triangle} = 6 \, \text{in} + 7 \, \text{in} + 12 \, \text{in} = 25 \, \text{in}
\]

Next, we use the ratio of the perimeters to find the scale factor:

\[
\text{Scale factor} = \frac{\text{Perimeter of larger triangle}}{\text{Perimeter of smaller triangle}} = \frac{75 \, \text{in}}{25 \, \text{in}} = 3
\]

This means that each side of the larger triangle is three times the corresponding side of the smaller triangle.

Now, we identify the shortest side of the smaller triangle, which is 6 in. We can now find the shortest side of the larger triangle:

\[
\text{Shortest side of larger triangle} = \text{Shortest side of smaller triangle} \times \text{Scale factor} = 6 \, \text{in} \times 3 = 18 \, \text{in}
\]

Thus, the length of the shortest side of the larger triangle is:

\[
\boxed{18 \, \text{in.}}
\]