To find the perimeter of the dilated triangle, we first need to determine the new side lengths after applying the scale factor of \( \frac{1}{3} \) to the original side lengths.
The original side lengths of the triangle are:
- \( 11 \) inches
- \( 9 \) inches
- \( 28 \) inches
Now, we will multiply each side length by the scale factor \( \frac{1}{3} \):
-
For the first side: \[ \text{New side}_1 = 11 \times \frac{1}{3} = \frac{11}{3} \text{ inches} \]
-
For the second side: \[ \text{New side}_2 = 9 \times \frac{1}{3} = 3 \text{ inches} \]
-
For the third side: \[ \text{New side}_3 = 28 \times \frac{1}{3} = \frac{28}{3} \text{ inches} \]
Now, we add these new side lengths to find the perimeter of the dilated triangle: \[ \text{Perimeter} = \frac{11}{3} + 3 + \frac{28}{3} \]
To add these fractions, we can express \( 3 \) as a fraction with a denominator of \( 3 \): \[ 3 = \frac{9}{3} \]
Now, we can add: \[ \text{Perimeter} = \frac{11}{3} + \frac{9}{3} + \frac{28}{3} = \frac{11 + 9 + 28}{3} = \frac{48}{3} = 16 \text{ inches} \]
Thus, the perimeter of the dilated triangle is: \[ \text{Perimeter} = \boxed{16} \text{ inches} \]
1 answer