Answer
19.1
Work Step by Step
Use the distance formula to find the length of each side.
$d_{AB}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{AB}=\sqrt{(0-(-2))^2+(5-(-2))^2}$
simplify in parentheses
$d_{AB}=\sqrt{(2)^2+(7)^2}$
simplify
$d_{AB}=\sqrt{4+49}$
$d_{AB}=\sqrt{53}$
$d_{AB}=7.3$
$d_{BC}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{BC}=\sqrt{(3-0)^2+(-1-5)^2}$
simplify in parentheses
$d_{BC}=\sqrt{(3)^2+(-6)^2}$
simplify
$d_{BC}=\sqrt{9+36}$
$d_{BC}=\sqrt{45}$
$d_{BC}=6.7$
$d_{AC}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
substitute given values
$d_{AC}=\sqrt{(3-(-2))^2+(-1-(-2))^2}$
simplify in parentheses
$d_{AC}=\sqrt{(5)^2+(1)^2}$
simplify
$d_{AC}=\sqrt{25+1}$
$d_{AC}=\sqrt{26}$
$d_{AC}=5.1$
The perimeter is the sum of the lengths of the sides.
$P=7.3+6.7+5.1=19.1$
