Question

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.

Answer 1

To find the length of a side of the square, calculate the square root of the sum of the areas of the circle (36 cm²) and the additional 12 cm². This results in a square side length of approximately 6.93 cm.

Step-by-step explanation:

We are given that the area of the circle is 36 cm², and we know that the area of a square is greater than the area of the circle by 12 cm², which means the area of the square is 36 cm² + 12 cm² = 48 cm².

The area of a square is given by A = a², where a is the length of the side of the square. So, we need to find the value of a that satisfies the equation a² = 48 cm².

By taking the square root of both sides of the equation, we get a = √(48 cm²). Simplifying the square root of 48 gives us a ≈ 6.93 cm. Therefore, the length of a side of the square is approximately 6.93 cm.

Answer 2

Area of the square: 36 cm^2 + 12cm^2
48cm^2

area of a square: side x side
48cm^2=side1^2 (sides of squares are all equal, so the same length is being multiplied by itself)

√ 48 cm^2

one side:
4√ 3 cm, or approximately 6.93cm