To determine the scale factor used in the dilation from triangle D to triangle D', we can compare the corresponding side lengths of both triangles.
The side lengths of triangle D are 24, 32, and 40.
The side lengths of triangle D' are 6, 8, and 10.
Now, we can find the scale factor by dividing the side lengths of triangle D' by the corresponding side lengths of triangle D:
\[ \text{Scale factor} = \frac{\text{length of D'}}{\text{length of D}} \]
Calculating the scale factors for each pair of corresponding sides:
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For the side of length 24 in triangle D: \[ \frac{6}{24} = \frac{1}{4} \]
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For the side of length 32 in triangle D: \[ \frac{8}{32} = \frac{1}{4} \]
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For the side of length 40 in triangle D: \[ \frac{10}{40} = \frac{1}{4} \]
Since all calculations yield the same scale factor, we determine that the scale factor used to dilate triangle D to create triangle D' is \(\frac{1}{4}\).
Therefore, the correct answer is: Scale factor of one fourth.