To find the perimeter of the dilated triangle, we first need to determine the lengths of the sides after dilation using the scale factor of 13.
The original side lengths of the triangle are:
- Side 1: 11 inches
- Side 2: 9 inches
- Side 3: 28 inches
We will multiply each side length by the scale factor (13) to find the new lengths:
- New Side 1: \( 11 \times 13 = 143 \) inches
- New Side 2: \( 9 \times 13 = 117 \) inches
- New Side 3: \( 28 \times 13 = 364 \) inches
Next, we calculate the perimeter of the dilated triangle by adding the new side lengths together:
\[ \text{Perimeter} = 143 + 117 + 364 \]
Calculating that sum:
\[ 143 + 117 = 260 \] \[ 260 + 364 = 624 \]
Thus, the perimeter of the dilated triangle is \( \boxed{624} \) inches.
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