The area of a square garden is 242m squared. How long is the diagonal?
The diagonal of a square of side s is s√2.
so, your side is √242, and the diagonal is √242√2 = √484 = 22m
To find the length of the diagonal of a square, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the square are equal in length, so we can call the length of one side of the square "s".
We know that the area of the square is 242 m², which means that each side has a length of the square root of 242.
To find the diagonal length (d), we can use the Pythagorean Theorem:
d² = s² + s²
d² = 2s²
Since we know that each side of the square is equal to the square root of 242, we can substitute this value in:
d² = 2(√242)²
d² = 2(242)
d² = 484
Taking the square root of both sides:
d = √484
d = 22
Therefore, the length of the diagonal of the square garden is 22 meters.
To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, the length of each side is equal.
Let's assume the length of one side of the square is "s".
According to the given information, the area of the square garden is 242 square meters. The formula for the area of a square is A = s^2, where A represents the area and s represents the length of one side.
Therefore, according to the given information, we have:
242 = s^2
To find the length of one side, we can take the square root of both sides of the equation:
√(242) = √(s^2)
This simplifies to:
15.556 = s
Now that we know the length of one side of the square (s = 15.556), we can find the length of the diagonal using the Pythagorean theorem.
In a square, the diagonal (d) forms a right triangle with two sides of equal length (s). Using the Pythagorean theorem, we have:
d^2 = s^2 + s^2
d^2 = 15.556^2 + 15.556^2
d^2 = 241.376 + 241.376
d^2 = 482.752
Taking the square root of both sides, we find:
d = √(482.752)
d ≈ 21.957
Therefore, the length of the diagonal of the square garden is approximately 21.957 meters.