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Explain Bot To find the diameter of the circle, we first need to understand the relationship between the circle and the square. Since the circle and square have the same area, their side lengths will also be equal. Let's assume that the side length of the square is equal to "x".
The area of a circle is calculated using the formula A = πr², where A is the area of the circle and r is the radius. The radius is half the diameter, so let's denote the radius of the circle as "r" and the diameter of the circle as "y".
To find the diameter of the circle, we need to solve for "y" using the information given.
Step 1: Find the area of the square:
The area of a square is calculated by squaring its side length. So, the area of the square is x².
Step 2: Set up an equation:
Since the area of the circle is equal to the area of the square, we can set up the equation:
πr² = x²
Step 3: Solve for "r":
To find the radius of the circle, we can rearrange the equation to solve for "r":
r = √(x²/π)
Step 4: Find the diameter "y":
The diameter is twice the radius, so we can calculate the diameter "y" by multiplying the radius by 2:
y = 2r = 2√(x²/π)
Now, if you know the value of "x", you can substitute it into this equation to find the diameter "y". Remember to round the answer to 2 decimal places if necessary.