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 20 m 20 m 6.32 m 6.32 m 18 m 18 m 28.28 m
The area of a square garden is given by the formula:
Area = Side^2
We can rearrange this formula to solve for the side length of the square:
Side = sqrt(Area)
Given that the area of the square garden is 400 m^2, we can substitute this value into the formula to find the side length:
Side = sqrt(400) = 20 m
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (d^2) is equal to the sum of the squares of the other two sides (a^2 + b^2).
In this case, the hypotenuse is the diagonal of the square garden, and the two sides are the side length of the square.
So, using the Pythagorean theorem, we can find the length of the diagonal:
d^2 = (side)^2 + (side)^2
d^2 = 20^2 + 20^2
d^2 = 400 + 400
d^2 = 800
Taking the square root of both sides, we can find the length of the diagonal:
d = sqrt(800) = 28.28 m
Therefore, the length of the diagonal of the square garden is 28.28 m.