Since the sides of a square are all the same, the area of a square can be found by Therefore, the side of the square must be The perimeter of a square can be found by adding up all of the four sides:

To solve, simply use the formula for the area of a square given side length s. Thus,

Based on the information given to you, you know that the area could be written as:

Likewise, you know that the perimeter is:

Now, isolate one of the values. For example, based on the second equation, you know:

Dividing everything by , you get:

Now, substitute this into the first equation:

To solve for , you need to isolate all of the variables on one side:

or:

Now, factor this:

, meaning that could be either or . These are the dimensions of your rectangle.

You could also get this answer by testing each of your options to see which one works for both the perimeter and the area.

To solve, simply multiply width and length. Thus,

To solve, simply use the formula for the area of a rectangle. Thus,

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

The long diagonal of a kite always bisects the short diagonal. Therefore, if one side of the bisected diagonal is inches, the entire diagonal is inches. It does not matter how long the long diagonal is.

To solve, simply use the formula for the area of a square given side length s. Thus,

To solve, simply use the formula for the area of a rectangle. Thus,

To solve, simply multiply width and length. Thus,