Find the perimeter of rectangle EFGH
, with vertices E(6,9)
and F(4,9)
, G(4,−5)
, and H(6,−5)
.
To find the perimeter of rectangle EFGH, we need to add up the lengths of all four sides.
Using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
The distance between points E and F:
dEF = sqrt((4 - 6)^2 + (9 - 9)^2) = sqrt((-2)^2 + 0^2) = sqrt(4) = 2
The distance between points F and G:
dFG = sqrt((4 - 4)^2 + (9 - (-5))^2) = sqrt(0^2 + 14^2) = sqrt(196) = 14
The distance between points G and H:
dGH = sqrt((6 - 4)^2 + (-5 - (-5))^2) = sqrt(2^2 + 0^2) = sqrt(4) = 2
The distance between points H and E:
dHE = sqrt((6 - 6)^2 + (-5 - 9)^2) = sqrt(0^2 + (-14)^2) = sqrt(196) = 14
Now add up the lengths of all four sides:
Perimeter = dEF + dFG + dGH + dHE
Perimeter = 2 + 14 + 2 + 14
Perimeter = 32
Therefore, the perimeter of rectangle EFGH is 32 units.