Question

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

Answer 1

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)))`