Question

triangle d gas been dilated to create d' determine the scale factor used
lenght of d' 8, 6 , 10
lenght of d 32, 24 40

Answer 1

To determine the scale factor used to dilate triangle \(D\) to triangle \(D'\), you can use the lengths of corresponding sides from both triangles. The scale factor \(k\) can be calculated by comparing the lengths of corresponding sides.

Given:
- Lengths of triangle \(D\): \(32\), \(24\), \(40\)
- Lengths of triangle \(D'\): \(8\), \(6\), \(10\)

You can calculate the scale factor \(k\) for each pair of corresponding sides:

1. For the side \(32\) in \(D\) corresponding to \(8\) in \(D'\):
\[
k_1 = \frac{8}{32} = \frac{1}{4}
\]

2. For the side \(24\) in \(D\) corresponding to \(6\) in \(D'\):
\[
k_2 = \frac{6}{24} = \frac{1}{4}
\]

3. For the side \(40\) in \(D\) corresponding to \(10\) in \(D'\):
\[
k_3 = \frac{10}{40} = \frac{1}{4}
\]

Since all three calculations give the same scale factor, the scale factor used to dilate triangle \(D\) to create triangle \(D'\) is:
\[
\text{Scale Factor } k = \frac{1}{4}
\]