find the perimeter of rectangle abcd with vertices a (1,7) b (4,7) c(4 -4) d (1 -4)
To find the perimeter of a rectangle, we add up the lengths of all four sides.
Let's find the lengths of each side:
Side AB:
AB = √((4-1)^2 + (7-7)^2) = √(3^2 + 0^2) = √9 = 3 units
Side BC:
BC = √((4-4)^2 + (-4-7)^2) = √(0^2 + 11^2) = √121 = 11 units
Side CD:
CD = √((1-1)^2 + (-4-7)^2) = √(0^2 + 11^2) = √121 = 11 units
Side DA:
DA = √((1-1)^2 + (7+4)^2) = √(0^2 + 11^2) = √121 = 11 units
Now, add up all the side lengths to get the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 3 + 11 + 11 + 11
Perimeter = 36 units
Therefore, the perimeter of rectangle ABCD is 36 units.