Given:
[tex]\Delta ABC\sim \Delta D E F[/tex]
[tex]AB=18,BC=21,AC=24,EF=7[/tex]
To find:
The scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex].
Solution:
We have,
[tex]\Delta ABC\sim \Delta D EF[/tex]
So, side BC is the corresponding side of EF.
Now, scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex] is
[tex]\text{Scale factor}=\dfrac{\text{ Side of }\Delta D EF}{\text{Corresponding side of }\Delta ABC}[/tex]
[tex]\text{Scale factor}=\dfrac{EF}{BC}[/tex]
[tex]\text{Scale factor}=\dfrac{7}{21}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]
Therefore, the scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex] is [tex]\dfrac{1}{3}[/tex].
