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?

Answer 1

To find the perimeter of the dilated triangle, you first need to apply the scale factor of \( \frac{1}{3} \) to each of the original side lengths of the triangle.

The side lengths of the original triangle are:
- 11 inches
- 9 inches
- 28 inches

Now, we can calculate the side lengths of the dilated triangle by multiplying each original side length by the scale factor \( \frac{1}{3} \):

1. For the side length of 11 inches:
\[
11 \times \frac{1}{3} = \frac{11}{3} \text{ inches}
\]

2. For the side length of 9 inches:
\[
9 \times \frac{1}{3} = 3 \text{ inches}
\]

3. For the side length of 28 inches:
\[
28 \times \frac{1}{3} = \frac{28}{3} \text{ inches}
\]

Now we have the new side lengths:
- \( \frac{11}{3} \) inches
- \( 3 \) inches
- \( \frac{28}{3} \) inches

Next, let's find the perimeter of the dilated triangle by summing the new side lengths:

\[
\text{Perimeter} = \frac{11}{3} + 3 + \frac{28}{3}
\]

First, convert \( 3 \) into a fraction with a common denominator of 3:
\[
3 = \frac{9}{3}
\]

Now add them together:
\[
\text{Perimeter} = \frac{11}{3} + \frac{9}{3} + \frac{28}{3} = \frac{11 + 9 + 28}{3} = \frac{48}{3} = 16 \text{ inches}
\]

Thus, the perimeter of the dilated triangle is \( \boxed{16} \) inches.