Answer:
P ≈ 25 units
Step-by-step explanation:
LM = 12 units ( horizontal line )
use the distance formula to find length of other 2 sides.
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = L (- 3, 2) and (x₂, y₂ ) = M (3, 5 )
LM = [tex]\sqrt{3-(-3))^2+(5-2)^2}[/tex]
= [tex]\sqrt{(3+3)^2+3^2}[/tex]
= [tex]\sqrt{6^2+9}[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
Repeat with (x₁, y₁ ) = M (3, 5) and (x₂, y₂ ) = N (9, 2)
MN = [tex]\sqrt{(9-3)^2+(2-5)^2}[/tex]
= [tex]\sqrt{6^2+(-3)^2}[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
Then perimeter P is the sum of the 3 sides
P = 12 + [tex]\sqrt{45}[/tex] + [tex]\sqrt{45}[/tex] = 12 + 2[tex]\sqrt{45}[/tex] ≈ 25 units ( to the nearest unit )
