Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.
That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).
Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.
[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]
I've marked corresponding sides and angles in the attached picture.
