The area of a square garden is 400 m 2
. How long is the diagonal? Round your answer to the hundredths place. (1 point)
Responses
28.28 m
28.28 m
18 m
18 m
20 m
20 m
6.32 m
6.32 m
To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, the diagonal is the hypotenuse of a right triangle, where the sides of the triangle are the length of one side of the square.
Let x represent the length of one side of the square.
Using the Pythagorean theorem, we have:
x^2 + x^2 = diagonal^2
Simplifying, we have:
2x^2 = diagonal^2
Taking the square root of both sides, we have:
√(2x^2) = diagonal
Simplifying further, we have:
√2 * x = diagonal
Given that the area of the square is 400 m^2, we can solve for x:
x^2 = 400
x = √400
x = 20 m
Substituting the value of x into the equation for the diagonal, we have:
diagonal = √2 * 20
diagonal = 20√2
Rounding to the hundredths place, the length of the diagonal is approximately 28.28 m.
Therefore, the correct answer is:
28.28 m.