The problem states that the area of a rectangle with sides 12 cm and 8 cm is equal to the area of a square. The question asks for the length of a side of the square.

1. Problem Description

The problem states that the area of a rectangle with sides 12 cm and 8 cm is equal to the area of a square. The question asks for the length of a side of the square.

2. Solution Steps

First, we calculate the area of the rectangle. The area of a rectangle is given by:

$Area = length \times width$

$Area_{rectangle} = 12 \text{ cm} \times 8 \text{ cm} = 96 \text{ cm}^2$

Next, we know that the area of the square is equal to the area of the rectangle.

$Area_{square} = Area_{rectangle} = 96 \text{ cm}^2$

The area of a square is given by:

$Area = side \times side = side^2$

So we have

$side^2 = 96 \text{ cm}^2$

To find the length of the side of the square, we take the square root of the area:

$side = \sqrt{96}$

$side = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}$

Therefore, the length of a side of the square is $4\sqrt{6}$ cm.

3. Final Answer

The side length of the square is $4\sqrt{6}$ cm.