Answer:
The perimeter of the triangle is approximately equal to 18
Step-by-step explanation:
The coordinates of the vertices of the triangle are (-3, -1), (2, 3), and (5, 2)
The formula for the lengths, l, of the sides of the triangle, given their end points coordinates is presented as follows;
![l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}](https://tex.z-dn.net/?f=l%20%3D%20%5Csqrt%7B%5Cleft%20%28y_%7B2%7D-y_%7B1%7D%20%20%5Cright%20%29%5E%7B2%7D%2B%5Cleft%20%28x_%7B2%7D-x_%7B1%7D%20%20%5Cright%20%29%5E%7B2%7D%7D)
The lengths of the segments that make up the triangle are therefore;
Between the vertex points (-3, -1) and (2, 3), we have, √((-3 - 2)² + (-1 - 3)²) = √41
Between the vertex points (-3, -1) and (5, 2), we have, √((-3 - 5)² + (-1 - 2)²) = √73
Between the vertex points (2, 3) and (5, 2), we have, √((2 - 5)² + (3 - 2)²) = √10
Therefore;
The perimeter of the triangle = The sum of the lengths of the sides of the triangle = √41 + √73 + √10
The perimeter of the triangle = √41 + √73 + √10 ≈ 18.1094
∴ The perimeter of the triangle ≈ 18, after rounding to the nearest whole number.