The coordinates of he 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 if necessary)

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the perimeter of triangle PQR, hence, you need to find the lengths of the sides of triangle, using distance formula, such that:

`PQ = sqrt((x_Q - x_P)^2 + (y_Q - y_P)^2)`

`PQ = sqrt(4 + 64) => PQ = sqrt 68 = 2sqrt17`

`PR = sqrt((x_R - x_P)^2 + (y_R - y_P)^2)`

`PR = sqrt(9 + 9) => PR = sqrt18 = 3sqrt2`

`RQ = sqrt((x_Q - x_R)^2 + (y_Q - y_R)^2)`

`RQ = sqrt(25 + 25) => RQ = 5sqrt2`

Evaluating the perimeter of triangle PQR yields:

`P_(PQR) = PQ + QR + PR => P_(PQR) = 2sqrt17 + 5sqrt2 + 3sqrt2`

Combining the members that contain the same radical, yields:

`P_(PQR) = 2sqrt17 + 8sqrt2`

Factoring out 2 yields:

`P_(PQR) = 2(sqrt17 + 4sqrt2) => P_(PQR) = 2(sqrt17 + sqrt(4^2*2))`

`P_(PQR) = 2(sqrt17 + sqrt32)`

Hence, evaluating the perimeter of triangle PQR, using distance formula, yields `P_(PQR) = 2(sqrt17 + sqrt32).`