Answer:
9.84 units.
Step-by-step explanation:
We will use distance formula to find the perimeter of the given triangle.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\text{Distance between B and D}=\sqrt{(2-1)^2+(4-2)^2}[/tex]
[tex]\text{Distance between B and D}=\sqrt{(1)^2+(2)^2}[/tex]
[tex]\text{Distance between B and D}=\sqrt{1+4}[/tex]
[tex]\text{Distance between B and D}=\sqrt{5}[/tex]
[tex]\text{Distance between D and E}=\sqrt{(5-2)^2+(2-4)^2}[/tex]
[tex]\text{Distance between D and E}=\sqrt{(3)^2+(-2)^2}[/tex]
[tex]\text{Distance between D and E}=\sqrt{9+4}[/tex]
[tex]\text{Distance between D and E}=\sqrt{13}[/tex]
We can see the distance between B and E is 4 units (5-1).
[tex]\text{Perimeter of triangle BDE}=\sqrt{5}+\sqrt{13}+4[/tex]
[tex]\text{Perimeter of triangle BDE}=9.841619252\approx 9.84[/tex]
Therefore, the perimeter of triangle BDE is 9.84 units.
