Final answer:
To find the perimeter of the rectangle ABCD, calculate the lengths of sides AB and BC using the distance formula, then double both lengths to account for opposite equal sides, and sum them to get the approximate perimeter of 40.24 units.
Step-by-step explanation:
To find the approximate perimeter of the rectangle with vertices at points B(4,5), A(-6,0), C(8,-3), and D(-2,-8), we must first determine the lengths of the sides of the rectangle using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by √((x2 - x1)² + (y2 - y1)²).
First, we calculate the distance between points A and B to find the length of one side. And then we calculate the distance between points B and C for the length of another side. Since a rectangle has opposite sides of equal length, we need only calculate two adjacent sides. The formula would be applied as follows:
- AB = √((-6 - 4)² + (0 - 5)²) = √((-10)² + (-5)²) = √(100 + 25) = √(125)
- BC = √((8 - 4)² + (-3 - 5)²) = √((4)² + (-8)²) = √(16 + 64) = √(80)
Since the lengths of the other two sides (AD and CD) are equal to AB and BC respectively, we can determine the approximate perimeter by adding together the lengths of all four sides:
Perimeter = AB + BC + AD + CD = 2(AB) + 2(BC) = 2√(125) + 2√(80)
Substituting the approximate root values:
Perimeter ≈ 2(11.18) + 2(8.94) ≈ 22.36 + 17.88 ≈ 40.24 units
Therefore, the approximate perimeter of the given rectangle is 40.24 units.