Use the distance formula or Pythagorean Theorem to find the length of each of the sides.
(-5, -4) to (2, 6)
d = [tex]\sqrt{(-5 - 2)^{2} + (-4 - 6)^{2} }[/tex]
= [tex]\sqrt{(- 7)^{2} + (-10)^{2} }[/tex]
= [tex]\sqrt{49 + 100}[/tex]
= [tex]\sqrt{149}[/tex]
(2, 6) to (4, -4)
d = [tex]\sqrt{(2 - 4)^{2} + (6 - (-4))^{2} }[/tex]
= [tex]\sqrt{(- 2)^{2} + (10)^{2} }[/tex]
= [tex]\sqrt{4 + 100}[/tex]
= [tex]\sqrt{104}[/tex]
= 2[tex]\sqrt{26}[/tex]
(-5, -4) to (4, -4)
you can just count the distance between the coordinates: d = 9
Perimeter = (-5, -4) to (2, 6) + (2, 6) to (4, -4) + (-5, -4) to (4, -4)
= [tex]\sqrt{149}[/tex] + 2[tex]\sqrt{26}[/tex] + 9
Answer: [tex]\sqrt{149}[/tex] + [tex]\sqrt{149}[/tex] + 9
