20 pts The vertices of a triangle are (3,-2), (5.-8) and (-2, 1). What is the approximate perimeter of
the triangle

23.56 length units

Step-by-step explanation:

To calculate the perimeter of a triangle, we need to calculate the length of all the sides, then sum up the lengths.

To calculate each side, we take the differences of the coordinates of consecutive vertices, square, add, and take square-root (Pythagoras theorem).

Side 1: (3,-2), (5, -8)

difference in coordinates=(2,-6), length=sqrt(2^2+6^2) = sqrt(40)

Side 2: (5, -8), (-2,1)

difference in coordinates=(7,-9), length=sqrt(7^2+9^2) = sqrt(130)

Side 2: (-2,1), (3,-2)

difference in coordinates=(5,-3), length=sqrt(5^2+3^2) = sqrt(34)

Perimeter

= sum of sides

= sqrt(40)+sqrt(130)+sqrt(34)

= 6.32+11.40+5.83

= 23.56 approximately