The area of a square is greater than the area of the circle by 12 cm². Find the length of the side of a square if the area of the circle is 36 cm².

36+12=48

Side of square is √48 which is 4√3
Logic

Answer: 4√3

First you find the total area of the square:
which is the area of the circle + 12
36+12= 48 cm^2

Next you need to find the side of the square. We know that all sides of a square are equal and we know the area of the square is 48 cm^2. The area of a square is the side^2. So we know the side is equal to the square root of the area:
√48. If you want to simplify that you can do 4√3 !!

Hope this helps!

To find the length of the side of the square, we need to use the information given in the problem. Let's break it down step by step.

1. Let's assume the length of one side of the square is "x" cm. Since a square has four equal sides, the area of the square can be calculated as x² cm².

2. We are given that the area of the circle is 36 cm². The formula for the area of a circle is A = πr², where A is the area and r is the radius.

3. To find the radius, we can solve for it using the formula for the area of the circle. The area of the circle is given as 36 cm², so we have:
36 = πr²

4. Divide both sides of the equation by π to isolate the radius:
r² = 36/π

5. Take the square root of both sides to find the value of the radius:
r = √(36/π)

6. Now that we have the radius, we can substitute it into the formula for the area of the square to find the length of the side:
x² = A(square) = (r + √12)²

7. Now we need to simplify the equation and solve for x. Expanding the square of a binomial gives us:
x² = r² + 2r√12 + 12

8. Let's substitute the value of r with √(36/π) and solve for x:
x² = (36/π) + 2(√(36/π))√12 + 12

9. Simplify the equation further. Since we know the value of the area of the circle is 36 cm², we can substitute that value into the equation:
x² = 36/π + 2(√(36/π))√12 + 12

10. Now we have an equation to solve for x. Use a calculator to find the value of the right-hand side of the equation and then take the square root of that expression to solve for x.

By following these steps, you should be able to find the length of the side of the square.

s^2 = 36+12

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