Question

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 Skip to navigation

Answer 1

To find the perimeter of the dilated triangle, you first need to determine the new lengths of the sides after applying the dilation scale factor of \( \frac{1}{3} \).

Given the original side lengths of the triangle are 11 inches, 9 inches, and 28 inches, you can calculate the new lengths as follows:

1. New length of the first side:
\[
\text{New length} = 11 \times \frac{1}{3} = \frac{11}{3} \approx 3.67 \text{ inches}
\]

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

3. New length of the third side:
\[
\text{New length} = 28 \times \frac{1}{3} = \frac{28}{3} \approx 9.33 \text{ inches}
\]

Now, you can calculate the perimeter of the dilated triangle by adding up the new side lengths:

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

To combine these, convert 3 into a fraction with a 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 **16 inches**.