Question

Suppose you dilate a triangle using the scale factor of 1/3 . The original side lengths of the triangle measure 11,9 and 28 inches. What is the perimeter of the dilated triangle?(1 point) perimeter =  in

Answer 1

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 \( \frac{1}{3} \):

1. For the first side:
\[
\text{New side}_1 = 11 \times \frac{1}{3} = \frac{11}{3} \text{ inches}
\]

2. For the second side:
\[
\text{New side}_2 = 9 \times \frac{1}{3} = 3 \text{ inches}
\]

3. 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:
\[
\text{Perimeter} = \boxed{16} \text{ inches}
\]