A gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.
a. 16√8
b. 2√8
c. 8√2
d. 4
To find the length of the diagonal side of a square, we can use the Pythagorean theorem.
The Pythagorean theorem states that for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, the two legs of the right triangle formed by dividing the square diagonally in half are of equal length, since it is a square.
Let's call the length of each leg x. Then, according to the Pythagorean theorem, we have:
x^2 + x^2 = (8)^2
2x^2 = 64
x^2 = 32
Taking the square root of both sides, we get:
x = sqrt(32)
x = sqrt(16 * 2)
x = 4sqrt(2)
Therefore, the length of each leg (and the diagonal side) is 4sqrt(2), so the answer is c. 8√2.