Answer:
The perimeter of triangle is 19.8 units
Step-by-step explanation:
we know that
The perimeter of triangle ABC is
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
we have
[tex]A(-2,3),B(3,0)[/tex]
substitute in the formula
[tex]d=\sqrt{(0-3)^{2}+(3+2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(5)^{2}}[/tex]
[tex]d_A_B=\sqrt{34}\ units[/tex]
step 2
Find the distance BC
we have
[tex]B(3,0),C (-4,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-0)^{2}+(-4-3)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-7)^{2}}[/tex]
[tex]d_B_C=\sqrt{58}\ units[/tex]
step 3
Find the distance AC
we have
[tex]A(-2,3),C (-4,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-3)^{2}+(-4+2)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(-2)^{2}}[/tex]
[tex]d_A_C=\sqrt{40}\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=\sqrt{34}+\sqrt{58}+\sqrt{40}[/tex]
[tex]P=19.8\ units[/tex]
