Answer: 19.8 Units
Step-by-step explanation:
The triangle is shown in the attached figure, and have three vertices: [tex]AB[/tex], [tex]AC[/tex] and [tex]BC[/tex].
Each vertice represents a point in the cartesian plane and the length of each side of the triangle is the modulus of each vector.
In this sense, the modulus [tex]m[/tex] is calculated as shown:
[tex]m=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]
Hence, for each vector:
[tex]AB=\sqrt{(-2-3)^{2} + (3-0)^{2}}=\sqrt{34}[/tex]
[tex]AC=\sqrt{(-2-(4))^{2} + (3-(-3))^{2}}=\sqrt{40}[/tex]
[tex]BC=\sqrt{(-4-3)^{2} + (-3-0)^{2}}=\sqrt{58}[/tex]
Now, the perimeter of a triangle is the sum of its three sides:
[tex]AB+AC+BC=\sqrt{34} + \sqrt{40} + \sqrt{58}[/tex]
Finally:
[tex]AB+AC+BC=19.77 \approx 19.8[/tex]
