To find the perimeter of the dilated triangle, we first need to calculate the new side lengths after applying the scale factor of \( \frac{1}{2} \).
The original side lengths of the triangle are:
- \( 7 \) inches
- \( 8 \) inches
- \( 10 \) inches
Now, we will multiply each side length by the scale factor \( \frac{1}{2} \):
-
For the side measuring \( 7 \) inches: \[ 7 \times \frac{1}{2} = \frac{7}{2} = 3.5 \text{ inches} \]
-
For the side measuring \( 8 \) inches: \[ 8 \times \frac{1}{2} = \frac{8}{2} = 4 \text{ inches} \]
-
For the side measuring \( 10 \) inches: \[ 10 \times \frac{1}{2} = \frac{10}{2} = 5 \text{ inches} \]
Now, we have the side lengths of the dilated triangle:
- \( 3.5 \) inches
- \( 4 \) inches
- \( 5 \) inches
Next, we calculate the perimeter of the dilated triangle by adding these new side lengths together: \[ \text{Perimeter} = 3.5 + 4 + 5 \]
Calculating this gives: \[ \text{Perimeter} = 12.5 \text{ inches} \]
Thus, the perimeter of the dilated triangle is \( \boxed{12.5} \) inches.
1 answer