The area of a square garden is 200 m² how long is the diagonal?

Answer 1

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.