Step 1. Calculate the perimeter of triangle DEF:
[tex]\begin{gathered} \text{Perimeter DEF=}12+15+21 \\ \text{Perimeter DEF=48} \end{gathered}[/tex]
Step 2. Calculate the perimeter of triangle ABC:
[tex]\begin{gathered} \text{Perimeter ABC=}8+10+14 \\ \text{Perimeter ABC=32} \end{gathered}[/tex]
Step 3. Divide the perimeters to find the ratio:
[tex]\text{ratio perimeter DEF to }ABC=\frac{Perimeter\text{ DEF}}{Perimeter\text{ ABC}}[/tex]
The result is:
[tex]\frac{48}{32}[/tex]
Step 4. Simplify the result:
[tex]\frac{48}{32}=\frac{3}{2}=1.5[/tex]
Answer: 1.5
