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

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

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

, where one of the two missing sides.

All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.

Similarly, the two bottom angles are equal to each other as well.

Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:

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.

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.

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

, where one of the two missing sides.

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

, where one of the two missing sides.

By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side with a length of , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

Note: the correct solution can also be found by:

The original formula used in this solution is an application of the Distributive Property: