Answer:
10 + 2[tex]\sqrt{58}[/tex]
Step-by-step explanation:
perimeter of DEFG = DE + EF + FG + DG
DE, EF, FG, and DG are all hypotenuse.
DE =[tex]\sqrt[]{4^{2} + 3^{2} }[/tex] = 5
EF = [tex]\sqrt{4^{2}+3^{2} }[/tex] = 5
FG = [tex]\sqrt{3^{2} +7^{2} }[/tex] = [tex]\sqrt{58}[/tex]
DG = [tex]\sqrt{3^{2}+7^{2} }[/tex] = [tex]\sqrt{58}[/tex]
DE + EF + FG + DG
= 5 + 5 + [tex]\sqrt{58}[/tex] + [tex]\sqrt{58}[/tex]
= 10 + 2[tex]\sqrt{58}[/tex]