Answer:
4 + 4√2
Step-by-step explanation:
[tex]CD=\sqrt{\left( 4-4\right)^{2} +\left( -5 - (-1)\right)^{2} } \\\\\\ =\sqrt{\left( 0\right)^{2} +(-4)^{2} }\\\\\\\ = \sqrt{16 }\\\\\\ =4[/tex]
[tex]DE=\sqrt{\left( 2-4\right)^{2} +\left( -3 - (-5)\right)^{2} } \\\\\\ =\sqrt{\left(-2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}[/tex]
[tex]\text{\bf{EC} $=\sqrt{\left( 4-2\right)^{2} +\left( -1 - (-3)\right)^{2} } \\\\\\ =\sqrt{\left( 2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}$}[/tex]
Perimeter (∆CDE) = CD + DE + EC
= 4 + 2√2 + 2√2
= 4 + 4√2
≈ 9.7
