To find the perimeter of the dilated triangle, you first need to determine the new lengths of the sides after applying the dilation scale factor of \( \frac{1}{3} \).
Given the original side lengths of the triangle are 11 inches, 9 inches, and 28 inches, you can calculate the new lengths as follows:
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New length of the first side: \[ \text{New length} = 11 \times \frac{1}{3} = \frac{11}{3} \approx 3.67 \text{ inches} \]
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New length of the second side: \[ \text{New length} = 9 \times \frac{1}{3} = \frac{9}{3} = 3 \text{ inches} \]
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New length of the third side: \[ \text{New length} = 28 \times \frac{1}{3} = \frac{28}{3} \approx 9.33 \text{ inches} \]
Now, you can calculate the perimeter of the dilated triangle by adding up the new side lengths:
\[ \text{Perimeter} = \frac{11}{3} + 3 + \frac{28}{3} \]
To combine these, convert 3 into a fraction with a denominator of 3:
\[ 3 = \frac{9}{3} \]
Now, add them together:
\[ \text{Perimeter} = \frac{11}{3} + \frac{9}{3} + \frac{28}{3} = \frac{11 + 9 + 28}{3} = \frac{48}{3} = 16 \text{ inches} \]
Thus, the perimeter of the dilated triangle is 16 inches.
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