To find the perimeter of the dilated triangle, we first need to calculate the new side lengths after applying the scale factor of 1.5 to each of the original side lengths.
The original side lengths of the triangle are 7 inches, 12 inches, and 9 inches. We will multiply each side length by the scale factor:
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For the first side: \[ 7 \text{ inches} \times 1.5 = 10.5 \text{ inches} \]
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For the second side: \[ 12 \text{ inches} \times 1.5 = 18 \text{ inches} \]
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For the third side: \[ 9 \text{ inches} \times 1.5 = 13.5 \text{ inches} \]
Now we have the dilated side lengths: 10.5 inches, 18 inches, and 13.5 inches.
Next, we calculate the perimeter of the dilated triangle by summing the new side lengths:
\[ \text{Perimeter} = 10.5 + 18 + 13.5 \]
Now, performing the addition step-by-step:
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First, sum 10.5 and 18: \[ 10.5 + 18 = 28.5 \]
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Next, add 13.5 to the result: \[ 28.5 + 13.5 = 42 \]
Therefore, the perimeter of the dilated triangle is
\[ \boxed{42} \text{ inches}. \]
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