Answer
No, the two triangles are not similar. Only two of the sides have the same scale factor or ratio, so the two triangles are not similar.
Work Step by Step
We are given the measures of all the sides in the two triangles. Let's see if the Side-Side-Side Similarity Theorem can be applied here.
The SSS Similarity Theorem states that if three sides in one triangle are proportional to the three sides of another triangle, then the two triangles are similar.
Let's set up the ratios of corresponding sides in $\triangle ABC$ and $\triangle DEF$:
$\frac{AB}{DE} = \frac{32}{24}$
Divide the numerator and denominator by their greatest common factor, $8$:
$\frac{AB}{DE} = \frac{4}{3}$
Let's look at $BC$ and $EF$:
$\frac{BC}{EF} = \frac{24}{18}$
Divide the numerator and denominator by their greatest common factor, $6$:
$\frac{BC}{KG} = \frac{4}{3}$
Let's look at $CA$ and $FD$:
$\frac{CA}{FD} = \frac{48}{38}$
Divide the numerator and denominator by their greatest common factor, $2$:
$\frac{CA}{FD} = \frac{24}{19}$
No, the two triangles are not similar. Only two of the sides have the same scale factor or ratio, so the two triangles are not similar.
