Final answer:
The perimeter of triangle PQR cannot be calculated with only one vertex given. In contrast, the perimeter of a rectangle or square can be calculated using the formula P = 2l + 2w when length and width are known.
Step-by-step explanation:
To calculate the perimeter of a polygon, we need the length of all its sides. However, for the triangle PQR with vertex P(-2,9), we do not have enough information to determine its perimeter. To find this, we would need the coordinates of the other two vertices Q and R. Once all three coordinates are known, we can use the distance formula to find the lengths of the sides PQ, QR, and RP.
Let's take another example: If we know the lengths of a town square are 39.2 meters and 17.5 meters, then the perimeter can be calculated using the formula P = 2l + 2w, where 'l' is the length and 'w' is the width. For the town square, the perimeter would be 2(39.2 meters) + 2(17.5 meters), resulting in a perimeter of 113.4 meters.
Similarly, if we have coordinates of two points, like P₁ (2.165 m, 1.250 m) and P₂(−1.900 m, 3.290 m), we can calculate the distance between them, which is a length of one side of a polygonal shape. This information is essential for computing the full perimeter when all side lengths are known. We also see example calculations dealing with vectors and their magnitudes which are relevant in physics or advanced mathematics, but these are for different contexts and do not directly apply to calculating the perimeter of a triangle.