Rectangle EFGH has verticles at E(7,7), F(1,5), G(2,2), and H(8,4).

EF = √((1-7)^2 + (5-7)^2) = √(36+4) = √40 = 2√10

Find the other lengths in like wise, then add them up.
Looks like C or D will be the answer.

thank you

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To find the perimeter of rectangle EFGH, we need to calculate the lengths of its four sides and add them together.

The length of a side can be found using the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of the sides:

Side EF:
(x1, y1) = (7, 7)
(x2, y2) = (1, 5)

d = sqrt((1 - 7)^2 + (5 - 7)^2)
= sqrt((-6)^2 + (-2)^2)
= sqrt(36 + 4)
= sqrt(40)

Side FG:
(x1, y1) = (1, 5)
(x2, y2) = (2, 2)

d = sqrt((2 - 1)^2 + (2 - 5)^2)
= sqrt((1)^2 + (-3)^2)
= sqrt(1 + 9)
= sqrt(10)

Side GH:
(x1, y1) = (2, 2)
(x2, y2) = (8, 4)

d = sqrt((8 - 2)^2 + (4 - 2)^2)
= sqrt((6)^2 + (2)^2)
= sqrt(36 + 4)
= sqrt(40)

Side HE:
(x1, y1) = (8, 4)
(x2, y2) = (7, 7)

d = sqrt((7 - 8)^2 + (7 - 4)^2)
= sqrt((-1)^2 + (3)^2)
= sqrt(1 + 9)
= sqrt(10)

Now, let's add up the lengths of all four sides:

Perimeter = EF + FG + GH + HE
= sqrt(40) + sqrt(10) + sqrt(40) + sqrt(10)

Simplifying the square roots:

Perimeter = 2sqrt(10) + 2sqrt(40)

Since sqrt(10) can be simplified as 2sqrt(10) and sqrt(40) can be simplified as 2sqrt(10)√2:

Perimeter = 2sqrt(10) + 2(sqrt(10)√2)
= 2sqrt(10) + 2√(10*2)
= 2sqrt(10) + 2√20
= 2sqrt(10) + 2(2√5)
= 2sqrt(10) + 4√5

Comparing the answer choices, we see that the closest option is:

B. 10√13

Therefore, the perimeter of rectangle EFGH is 10√13 units.