Answer:
[tex]35.6\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of triangle is equal to the sum of the length of the three sides
Let
[tex]A(7, 1), B(-6, 1), C(10, 6)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(7, 1), B(-6, 1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1-1)^{2}+(-6-7)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-13)^{2}}[/tex]
[tex]dAB=13\ units[/tex]
Find the distance BC
[tex]B(-6, 1), C(10, 6)[/tex]
substitute in the formula
[tex]d=\sqrt{(6-1)^{2}+(10+6)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(16)^{2}}[/tex]
[tex]dBC=16.8\ units[/tex]
Find the distance AC
[tex]A(7, 1), C(10, 6)[/tex]
substitute in the formula
[tex]d=\sqrt{(6-1)^{2}+(10-7)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(3)^{2}}[/tex]
[tex]dAC=5.8\ units[/tex]
Find the perimeter
[tex]P=dAB+dBC+dAC[/tex]
[tex]P=13+16.8+5.8=35.6\ units[/tex]
