The perimeter of a square is equal to the sum of the lengths of its four equally long sides, so the length of one side is one fourth of its perimeter. For this square, this is:

12 inches are equal to one foot, so divide by 12 to convert to feet:

The area of a square is equal to the square of the length of one side, so 

Area of a square in terms of each of its sides:

  Area = S x S

Perimeter of a square:

  Perimeter = 4S

So if 'the perimeter of a square is equal to twice its area':

  2 x Area = Perimeter

  2 x [S x S] = [4S]; divide by 2:

  S x S = 2S; divide by S:

  S = 2

To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in.  The perimeter of the square = 4s = 4 * 4 = 16 in.

Find the area of Square Y, then calculate the area of Square X.

If the perimeter of Square Y is 24, then each side is 24/4, or 6.

A = 6 * 6 = 36 sq ft, for Square Y

If Square X has 3 times the area, then 3 * 36 = 108 sq ft.

The area of the given square is given by so the side must be 6 in.  The side is reduced by a factor of two, so the new side is 3 in.  The perimeter of the new square is given by .

To solve, simply use the formula for the perimeter of a square.

Substitute in the side length of four into the following equation.

Thus,

To solve, simply use the formula for the perimeter of a square. Thus,

To solve, simply use the formula for the perimeter of the square. Thus,

If you don't remember the formula, you can simply sum the sides of a square to find the perimeter.

However, since all the sides area the same, we get the following.

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4.  Then take the square root of the area to get the length of one side, giving us 2.

Let x represent the length of the original square in inches.  Thus the area of the original square is x².  Two inches are added to x, which is represented by x+2.  The area of the resulting square is (x+2)².  We are given that the new square is 64 sq. inches greater than the original.  Therefore  we can write the algebraic expression:

x² + 64 = (x+2)²

FOIL the right side of the equation.

x² + 64 = x² + 4x + 4 

Subtract x² from both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares.  The choice with 15 would be correct because 17² -15² = 64.