Question

Suppose you dilate a triangle using the scale factor of 1/3
. The original side lengths of the triangle measure 11,9 and 28 inches. What is the perimeter of the dilated triangle?(1 point)
perimeter =

in

Answer 1

To find the perimeter of the dilated triangle, we first need to apply the scale factor of \( \frac{1}{3} \) to the original side lengths of the triangle.

The original side lengths are:
- \( 11 \) inches
- \( 9 \) inches
- \( 28 \) inches

Now, let's calculate the side lengths of the dilated triangle:

1. \( \text{Dilated side 1} = 11 \times \frac{1}{3} = \frac{11}{3} \) inches
2. \( \text{Dilated side 2} = 9 \times \frac{1}{3} = 3 \) inches
3. \( \text{Dilated side 3} = 28 \times \frac{1}{3} = \frac{28}{3} \) inches

Now, we find the perimeter of the dilated triangle by adding the dilated side lengths together:

\[
\text{Perimeter} = \frac{11}{3} + 3 + \frac{28}{3}
\]

First, we can convert \( 3 \) into a fraction with the same denominator:

\[
3 = \frac{9}{3}
\]

Now substituting this in:

\[
\text{Perimeter} = \frac{11}{3} + \frac{9}{3} + \frac{28}{3}
\]

Combine the fractions:

\[
\text{Perimeter} = \frac{11 + 9 + 28}{3} = \frac{48}{3} = 16
\]

Thus, the perimeter of the dilated triangle is:

\[
\text{Perimeter} = 16 \text{ inches}
\]