Find the perimeter of rectangle EFGH
, with vertices E(6,9)
and F(4,9)
, G(4,−5)
, and H(6,−5)
.(1 point)
units
To find the perimeter of a rectangle, we need to add up the lengths of all four sides.
The length of side EF is the distance between points E and F, which can be found using the distance formula:
EF = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 6)^2 + (9 - 9)^2)
= √((-2)^2 + 0^2)
= √(4 + 0)
= √4
= 2 units
Similarly, the length of side FG is the distance between points F and G:
FG = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 4)^2 + (9 - (-5))^2)
= √(0^2 + 14^2)
= √(0 + 196)
= √196
= 14 units
The length of side GH is the distance between points G and H:
GH = √((x2 - x1)^2 + (y2 - y1)^2)
= √((6 - 4)^2 + (-5 - (-5))^2)
= √(2^2 + 0^2)
= √(4 + 0)
= √4
= 2 units
Finally, the length of side HE is the distance between points H and E:
HE = √((x2 - x1)^2 + (y2 - y1)^2)
= √((6 - 6)^2 + (-5 - 9)^2)
= √(0^2 + (-14)^2)
= √(0 + 196)
= √196
= 14 units
To find the perimeter, we add up the lengths of all four sides:
Perimeter = EF + FG + GH + HE
= 2 + 14 + 2 + 14
= 32 units
Therefore, the perimeter of rectangle EFGH is 32 units.