Question
A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form
(1 point)
A.16sqrt(8)
B.2sqrt(8)
C.8sqrt(2)
D.4
(1 point)
A.16sqrt(8)
B.2sqrt(8)
C.8sqrt(2)
D.4
Answers
GPT 3.5
To find the length of the diagonal, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the two halves of the square lawn.
The length of each side of the square is 8 ft, so the length of the diagonal can be found using the equation:
diagonal^2 = side^2 + side^2
diagonal^2 = 8^2 + 8^2
diagonal^2 = 64 + 64
diagonal^2 = 128
Taking the square root of both sides gives us:
diagonal = sqrt(128)
Simplifying the square root:
diagonal = sqrt(64 * 2)
diagonal = sqrt(64) * sqrt(2)
diagonal = 8sqrt(2)
Therefore, the length of the diagonal is 8sqrt(2).
The correct answer is C. 8sqrt(2).
The length of each side of the square is 8 ft, so the length of the diagonal can be found using the equation:
diagonal^2 = side^2 + side^2
diagonal^2 = 8^2 + 8^2
diagonal^2 = 64 + 64
diagonal^2 = 128
Taking the square root of both sides gives us:
diagonal = sqrt(128)
Simplifying the square root:
diagonal = sqrt(64 * 2)
diagonal = sqrt(64) * sqrt(2)
diagonal = 8sqrt(2)
Therefore, the length of the diagonal is 8sqrt(2).
The correct answer is C. 8sqrt(2).