Rectangle ABCD has vertices point 4 (-5, 1), point B (-2, 1), pont C (-9, 6), and point D (-5, 6). Find the perimeter of the rectangle in feet
To find the perimeter of the rectangle, we need to add up the lengths of all four sides.
The length of side AB can be found using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(-2 - (-5))^2 + (1 - 1)^2]
AB = √[3^2 + 0^2]
AB = √(9) = 3
The length of side BC can also be found using the distance formula:
BC = √[(-9 - (-2))^2 + (6 - 1)^2]
BC = √[(-7)^2 + 5^2]
BC = √(49 + 25) = √74
The length of side CD can be found using the distance formula as well:
CD = √[(-5 - (-9))^2 + (6 - 6)^2]
CD = √[4^2]
CD = √16 = 4
The length of side DA can be found using the distance formula:
DA = √[(-5 - (-5))^2 + (6 - 1)^2]
DA = √[(0)^2 + 5^2]
DA = √25 = 5
Add up the lengths of all four sides to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 3 + √74 + 4 + 5
Perimeter ≈ 12.86 feet
Therefore, the perimeter of the rectangle ABCD is approximately 12.86 feet.