## Geometry: Common Core (15th Edition)

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. $P=7.3+6.7+5.1=19.1$