Question
The area of a square garden is 400 m2. How long is the diagonal? Round your answer to the hundredths place
Answers
GPT 3.5
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.
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.