Question

What is the perimeter of a triangle with corners at `(6 ,5 )`, `(8 ,2 )`, and `(4 ,7 )`?

Answer 1

Perimeter = 62

Explanation:

Let `(6,5)` = `A` , `(8,2)` = `B` and `(4,7)` = `C`
Formula of distance between points is :
`sqrt ((x_2-x_1)^2+(y_2-y_1)^2`
Find the distance between A and B:
Let `(6,5)` = `(x_1,y_1)` `and` `(8,2)` = `(x_2,y_2)`
`=>` `sqrt ((8-6)^2+(2-5)^2)`
`=>` `sqrt ((2)^2+(-3)^2)`
`=>` `sqrt ((4+9)^2)`
`=>` `sqrt ((13)^2)`
`=>` `13`

Find the distance between B and C:
Let `(8,2)` = `(x_1,y_1)` `and` `(4,7)` = `(x_2,y_2)`
`=>` `sqrt ((4-8)^2+(7-2)^2)`
`=>` `sqrt ((-4)^2+(5)^2)`
`=>` `sqrt ((16+25)^2)`
`=>` `sqrt ((41)^2)`
`=>` `41`

Find the distance between C and A:
Let `(4,7)` = `(x_1,y_1)` `and` `(6,5)` = `(x_2,y_2)`
`=>` `sqrt ((6-4)^2+(5-7)^2)`
`=>` `sqrt ((2)^2+(-2)^2)`
`=>` `sqrt ((4+4)^2)`
`=>` `sqrt ((8)^2)`
`=>` `8`

Perimeter = `AB + BC + CA`
`=>` `13 + 41 + 8`
`=>` `62`