A square has the same area as a rectangle whose longer side is 2 times the length of its shorter side. If the perimeter of the rectangle is 24, what is the perimeter of the square?

I have no idea how to do it. I need help.

Thanks.

To solve this problem, we need to find the dimensions of the rectangle first and then use that information to find the perimeter of the square.

Let's assume the shorter side of the rectangle is x. According to the problem, the longer side is two times the length of the shorter side, so the longer side of the rectangle is 2x.

To find the perimeter of the rectangle, we add up the four sides, which are the length, width, length, and width again. So, the perimeter of the rectangle is given by the equation:

Perimeter of the rectangle = 2(length + width)

Since the length is x and the width is 2x, we have:

Perimeter of the rectangle = 2(x + 2x) = 2(3x) = 6x.

According to the problem, the perimeter of the rectangle is given as 24, so we can set up an equation to solve for x:

6x = 24.

To solve for x, divide both sides of the equation by 6:

x = 24/6 = 4.

Now we know that the shorter side of the rectangle is 4, and the longer side is 2 times that, which is 8.

To find the area of the square, we use the formula:

Area of a square = side^2.

Since the area of the square is the same as the area of the rectangle, which is length times width, we have:

Area of the square = 4 * 8 = 32.

Now, to find the perimeter of the square, we need to find the length of its sides. Since it is a square, all sides are equal.

Using the formula for the area of a square, we know that the side^2 = 32. To find the side length (s), we take the square root of both sides:

s = √32.

Now, we can calculate the perimeter of the square using the formula:

Perimeter of the square = 4 * side length.

Substituting in the value of the side length:

Perimeter of the square = 4 * √32 = 4 * √(4 * 8) = 4 * (2√2) = 8√2.

Therefore, the perimeter of the square is 8√2.

rectangle:

2(x+2x) = 24
3x = 12
x = 4

So, the rectangle has area 2*4*8 = 64

Now, the square has side 8, so its perimeter is 32.