Question

What is the perimeter of a triangle with corners at `(9 ,2 )`, `(2 ,3 )`, and `(4 ,1 )`?

Answer 1

`sqrt50 +sqrt8 +sqrt26`

Explanation:

We know the distance between two points P(x1,y1) and Q(x2,y2) is given by PQ= `sqrt[(x2 -x1)^2 + (y2 - y1)^2]`
First we have to calculate the distance between (9,2)(2,3) ; (2,3)(4,1) and (4,1)(9,2) to get the lengths of the sides of triangles.
Hence lengths will be `sqrt[(2-9)^2+(3-2)^2] = sqrt[(-7)^2 + 1^2] = sqrt(49+1) = sqrt50`
`sqrt [(4-2)^2 +(1-3)^2] = sqrt[(2)^2 +(-2)^2] = sqrt[4+4]=sqrt8`
and
`sqrt[(9-4)^2 +(2-1)^2] = sqrt[5^2+1^2] = sqrt26`
Now the perimeter of the triangle is `sqrt50 +sqrt8 +sqrt26`