What is the perimeter of a triangle with corners at #(3 ,8)#, #(1 ,5 )#, and #(4 ,3 )#?

1 Answer
Sep 30, 2016

Perimeter:#color(magenta)(sqrt(13)(2+sqrt(2)))#

Explanation:

Distance from #color(red)(""(3,8))# to #color(blue)(""(1,5))#
#color(white)("XXX")d_1=sqrt((color(red)3-color(blue)1)^2+(color(red)8-color(blue)5)^2)=sqrt(4+9)=color(magenta)(sqrt(13))#

Distance from #color(blue)(""(1,5))# to #color(green)(""(4,3))#
#color(white)("XXX")d_2=sqrt((color(blue)1-color(green)4)^2+(color(blue)5-color(green)3)^2)=sqrt(9+4)=color(magenta)(sqrt(13))#

Distance from #color(green)(""(4,3))#to #color(red)(""(3,8))#
#color(white)("XXX")d_3=sqrt((color(green)4-color(red)3)^2+(color(green)3-color(red)8)^2)=sqrt(1+25)=color(magenta)(sqrt(26)=sqrt(2) * sqrt(13)#

#color(magenta)("Perimeter" = d_1+d_2+d_3#

#color(white)("XXX")=color(magenta)(2sqrt(13)+sqrt(2)sqrt(13))#

#color(white)("XXX")=color(magenta)(sqrt(13)(2+sqrt(2)))#