Answer:
≈38.57 units.
Explanation:
To find the perimeter of a rectangle, we need to add up the lengths of all its sides.
First, gather the coordinates:
R - (4, 5)
U - (8, -3)
F - (-6, 0)
O - (-2, -8)
Using the coordinates given, we can calculate the lengths of the sides of the rectangle using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
So, for the rectangle with vertices R, U, F, and O, we have:
Side RU: d = √((8 - 4)^2 + (-3 - 5)^2) = √(16 + 64) = √80
Side UF: d = √((-6 - 8)^2 + (0 - (-3))^2) = √(196 + 9) = √205
Side FO: d = √((-6 - (-2))^2 + (0 - (-8))^2) = √(16 + 64) = √80
Side OR: d = √((-2 - 4)^2 + (-8 - 5)^2) = √(36 + 169) = √205
Since opposite sides of a rectangle are congruent, we have RU = FO and UF = OR. Therefore, the perimeter of the rectangle is:
Perimeter = RU + UF + FO + OR
Perimeter = √80 + √205 + √80 + √205
Perimeter ≈ 38.57
Therefore, the perimeter of the rectangle is approximately 38.57 units.