Rectangle ABCD has vertices points A (-5,1) point B (-2,1) points C (-2,6) and points D (-5,6) find the perimeter of the rectangle in feet
To find the perimeter of the rectangle, we need to calculate the distance between each pair of adjacent points and then add all the distances together.
The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
√((x₂ - x₁)² + (y₂ - y₁)² )
Let's calculate the distances for each pair of points:
1. Distance between points A and B:
√((-2 - (-5))² + (1 - 1)² ) = √(3² + 0) = 3 feet
2. Distance between points B and C:
√((-2 - (-2))² + (6 - 1)² ) = √(0 + 5²) = 5 feet
3. Distance between points C and D:
√((-5 - (-2))² + (6 - 6)² ) = √(3² + 0) = 3 feet
4. Distance between points D and A:
√((-5 - (-5))² + (1 - 6)² ) = √(0 + 5²) = 5 feet
Now, add all the distances to find the perimeter:
Perimeter = 3 + 5 + 3 + 5 = 16 feet
Therefore, the perimeter of rectangle ABCD is 16 feet.
Same question but do it in square feet
To find the perimeter of the rectangle in square feet, we need to convert the distance values into square feet.
Given that the distances are already in feet, the perimeter calculated in the previous steps is already in feet.
Therefore, the perimeter of the rectangle ABCD is 16 feet.