Question

Suppose you dilate a triangle using a scale factor of 1/2.

The original side lengths of the triangle measure 7, 8, and 10 inches.



What is the perimeter of the dilated triangle?

Answer 1

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 \( \frac{1}{2} \):

1. For the side measuring \( 7 \) inches:
\[
7 \times \frac{1}{2} = \frac{7}{2} = 3.5 \text{ inches}
\]

2. For the side measuring \( 8 \) inches:
\[
8 \times \frac{1}{2} = \frac{8}{2} = 4 \text{ inches}
\]

3. 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.