Respuesta :
We have to find the length of each side. We can use the distance formula as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For side DE:
[tex]\begin{gathered} DE\text{ =}\sqrt[]{(7-5)^2+(5-6)^2} \\ DE\text{ =}\sqrt[]{4+1} \\ DE\text{ =}\sqrt[]{5} \end{gathered}[/tex]For side EF:
[tex]\begin{gathered} EF=\sqrt[]{(4-7)^2+(3-5)^2} \\ EF=\sqrt[]{9+4} \\ EF=\sqrt[]{13} \end{gathered}[/tex]For side DF:
[tex]\begin{gathered} DF=\sqrt[]{(4-5)^2+(3-6)^2} \\ DF=\sqrt[]{1+9} \\ DF=\sqrt[]{10} \end{gathered}[/tex]Finally, the perimeter of the triangle DEF is = √5 + √13 + √10 ≈ 9
