The area of a square garden is 200 m² how long is the diagonal?
Let's call the length of one side of the square "x". The area of a square is calculated by multiplying the length of one side by itself: x² = 200.
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the length of the hypotenuse (in this case, the diagonal of the square) is equal to the square root of the sum of the squares of the other two sides (in this case, two of the sides of the square).
So, we need to solve for x and then use it to find the length of the diagonal:
x² = 200
x = √200
x = 10√2 (rounded to two decimal places)
Now, we can use the Pythagorean theorem:
diagonal² = x² + x²
diagonal² = 2x²
diagonal = √(2x²)
diagonal = √(2(10√2)²)
diagonal = √(2(200))
diagonal = √400
diagonal = 20
So the length of the diagonal of the square garden is 20 meters.
To find the length of the diagonal of a square garden, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In a square, the diagonal is the hypotenuse, and the sides of the square are the other two sides of the right triangle.
Let's assume the length of one side of the square is "s."
The area of the square is given as 200 m². Since the area of a square is equal to the square of its side length, we can set up the equation:
s² = 200
To find the length of the side, we need to take the square root of both sides:
√(s²) = √200
s = √200
Now, we can find the length of the diagonal by using the Pythagorean theorem:
d² = s² + s²
d² = 2s²
Plugging in the value of "s" we found:
d² = 2(√200)²
d² = 2 * 200
d² = 400
Finally, taking the square root of both sides:
d = √400
d = 20
Therefore, the length of the diagonal of the square garden is 20 meters.