The area of a square garden is 400 m2. How long is the diagonal? Round your answer to the hundredths place
To find the length of the diagonal of a square, we can use the Pythagorean theorem.
Let's say the length of one side of the square is s.
The area of the square is given as 400 m^2.
We know that the formula for the area of a square is A = s^2.
So we can write the equation as s^2 = 400.
Taking the square root of both sides, we get s = √400.
Simplifying further, we get s = 20.
Now, we can use the Pythagorean theorem to find the length of the diagonal.
The diagonal of a square divides the square into two right-angled triangles. The diagonal is the hypotenuse, and the sides of the square are the legs.
Using the formula a^2 + b^2 = c^2,
we can write 20^2 + 20^2 = c^2, where c is the length of the diagonal.
Simplifying, we get 400 + 400 = c^2.
Combining like terms, we get 800 = c^2.
Taking the square root of both sides, we get c = √800.
Simplifying further, we get c = 28.28.
Therefore, the length of the diagonal of the square garden is approximately 28.28 meters.