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:
- \( \text{Dilated side 1} = 11 \times \frac{1}{3} = \frac{11}{3} \) inches
- \( \text{Dilated side 2} = 9 \times \frac{1}{3} = 3 \) inches
- \( \text{Dilated side 3} = 28 \times \frac{1}{3} = \frac{28}{3} \) 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:
\[ \text{Perimeter} = 16 \text{ inches} \]
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