To find the perimeter of the dilated triangle, first calculate the new side lengths after applying the scale factor of 1.5.
Given the original side lengths:
- Side 1: 7 inches
- Side 2: 12 inches
- Side 3: 9 inches
Now apply the scale factor of 1.5 to each side length:
- New Side 1: \( 7 \times 1.5 = 10.5 \) inches
- New Side 2: \( 12 \times 1.5 = 18 \) inches
- New Side 3: \( 9 \times 1.5 = 13.5 \) inches
Next, calculate the perimeter of the dilated triangle by adding the new side lengths: \[ \text{Perimeter} = 10.5 + 18 + 13.5 \]
Calculating step-by-step:
- \( 10.5 + 18 = 28.5 \)
- \( 28.5 + 13.5 = 42 \)
Thus, the perimeter of the dilated triangle is 42 inches.