Answer:
The perimeter is equal to [tex]16\ units[/tex]
Step-by-step explanation:
we have that
[tex]A(-1,1),B(2,5),C(5,1)[/tex]
The perimeter of triangle ABC is equal to
[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
[tex]A(-1,1),B(2,5)[/tex]
[tex]AB=\sqrt{(5-1)^{2}+(2+1)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
step 2
Find the distance BC
[tex]B(2,5),C(5,1)[/tex]
[tex]BC=\sqrt{(1-5)^{2}+(5-2)^{2}}[/tex]
[tex]BC=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]BC=\sqrt{25}[/tex]
[tex]BC=5\ units[/tex]
step 3
Find the distance AC
[tex]A(-1,1),C(5,1)[/tex]
[tex]AC=\sqrt{(1-1)^{2}+(5+1)^{2}}[/tex]
[tex]AC=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]AC=\sqrt{36}[/tex]
[tex]AC=6\ units[/tex]
step 4
Find the perimeter
[tex]P=5+5+6=16\ units[/tex]
