Question

What is the approximate perimeter of a triangle with vertices at (5, -1),(2, -5), and ( -3, -7)?

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\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) ~\hfill d1=√([ 2- 5]^2 + [ -5- (-1)]^2) \\\\\\ d1=√((-3)^2+(-5+1)^2)\implies d1=√(25)\implies \boxed{d1=5} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-7}) ~\hfill d2=√([ -3- 2]^2 + [ -7- (-5)]^2) \\\\\\ d2=√((-5)^2+(-7+5)^2)\implies d2=√(25+4)\implies \boxed{d2=√(29)} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill d3=√([ 5- (-3)]^2 + [ -1- (-7)]^2) \\\\\\ d3=√((5+3)^2+(-1+7)^2)\implies d3=√(100)\implies \boxed{d3=10} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{\large Perimeter}}{5+√(29)+10\implies 15+√(29)~~\approx~~20.39}`