Question

Find the perimeter of triangle ABC rounded to the nearest whole number. A (-1,4) B (2,2) and C (-2,-1)

Answer 1

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) ~\hfill AB=√((~~ 2- (-1)~~)^2 + (~~ 2- 4~~)^2) \\\\\\ ~\hfill AB=√(( 3)^2 + ( -2)^2)\implies \boxed{AB=√(13)} \\\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad C(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill BC=√((~~ -2- 2~~)^2 + (~~ -1- 2~~)^2)`

`~\hfill BC=√(( -4)^2 + ( -3)^2)\implies \boxed{BC=5} \\\\\\ C(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill CA=√((~~ -1- (-2)~~)^2 + (~~ 4- (-1)~~)^2) \\\\\\ ~\hfill CA=√(( 1)^2 + (5)^2)\implies \boxed{CA=√(26)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{√(13)~~ + ~~5~~ + ~~√(26) ~~ \approx ~~ \text{\LARGE 14}}`