Rectangle EFGH has verticles at E(7,7), F(1,5), G(2,2), and H(8,4).
How many units is the perimeter of rectangle EFGH.
Answer choices:
A. 20
B. 10√13
C. 5√10
D. 6√10
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
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.