# The coordinates of the vertices of Triangle PQR are P (0, -5), Q (-2,3) and R (3,-2). What is the perimeter of Triangle PQR? In simplest radical form.

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Expert Answers

jeew-m | Certified Educator

The length L between two coordinates (x1,y1) and (x2,y2) is given by;

`L = sqrt((x1-x2)^2+(y1-y2)^2)`

`P (0, -5)`

`Q (-2,3)`

`R (3,-2)`

Using the above we can find the lengths of PQ,PR and QR

`PQ = sqrt((0+2)^2+(-5-3)^2) = sqrt68 = sqrt(4xx17) = 2sqrt17`

`QR = sqrt((-2-3)^2+(3+2)^2) = sqrt50 = sqrt(25xx2) = 5sqrt2`

`PR = sqrt((0-3)^2+(-5+2)^2) = sqrt18 = sqrt(2xx9) = 3sqrt2`

Perimeter of triangle `= 2sqrt17+5sqrt2+3sqrt2 `

** Perimeter of triangle **` = 2sqrt17+8sqrt2 = 2(sqrt17+4sqrt2)`