Final answer:
To find the perimeter of the parallelogram, calculate the lengths of two adjacent sides using the distance formula and double the sum of these lengths. The lengths AB and AD are found to be √153 and 5 units, respectively. The perimeter is 2(√153 + 5) units.
Step-by-step explanation:
To find the perimeter of a parallelogram with vertices A(5,-6), B(2,6), C(1,-2), and D(8,-2), we need to calculate the lengths of two adjacent sides (since opposite sides are equal in a parallelogram) and then double this sum to get the total perimeter.
The distance formula to find the length between two points (x1, y1) and (x2, y2) is: Distance = √[(x2 - x1)^2 + (y2 - y1)^2].
Calculating AB and AD using the distance formula:
- AB = √[(2 - 5)^2 + (6 + 6)^2] = √[9 + 144] = √153
- AD = √[(8 - 5)^2 + (-2 + 6)^2] = √[9 + 16] = √25
Thus, the length of side AB is √153 units, and the length of side AD is 5 units. Since AB is equal to CD and AD is equal to BC in a parallelogram:
Perimeter = 2(AB + AD) = 2(√153 + 5)
So, the perimeter of the parallelogram is 2(√153 + 5) units.