To solve for the perimeter of the Quidditch field, we must first determine the length of the field. With the provided information, we can solve for this by drafting an algebraic equation:

Now that we know our length, we can determine the perimeter of the field:

A rectangle has the same length on either side and the same width on either side. Therefore if the football field has 100 yards in length and 50 yards in width you can use this formula.

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

If the formula escapes you, simply draw a picture and add all of the sides together. Rememeber, a rectangle has 4 sides, two are equal and the other 2 are equal.

First, we must solve for . The formula for the area of a rectangle is . Because we know the area is , and the length and width are  and , we can plug these in to solve for , as follows:

Since we know that , we can use this to solve for the sides of the rectangle:

and

We can now use these values to solve for the rectangle's perimeter:

Therefore, the perimeter of the rectangle is .

Not enough information is given to solve this problem. While  is a possible answer (assuming all of the sides of the rectangle are ), because it is a rectangle, you cannot assume that all of the sides are the same. Because  is not a prime number, there is more than one combination of numbers that could work out to equal an area of . 

Since we know the width and area, we can determine the length by using the equation for area of a rectangle:

Now that we know the length of the tile, we can solve for perimeter:

First we need to know that the square root of 4 is 2, we can know this because because if we work backwards we see that 2 x 2= 4, so we know the width of the rectangle is 2.

Since the length is 2 more than the width, we add 2 + 2 and get a length of 4 inches.

Now we can draw the rectangle and label each width (short side) with a measure of 2 inches and each length (long side) with a measure of 4 inches.

Now all we need to do is add up all the sides, so we have 2 + 2 + 4 + 4 which equals 12.

Since we are adding, and the measurements are in inches, our answer is .

For a rectangle, its perimeter is the sum of all for sides. We can write

Simplify

Solve for S

The given rectangle has a length that is  units longer than its width. This can be expressed in the following equation, where  is the length and  is the width of the rectangle.

Since the area of the rectangle is equal to its length multiplied by its width (), and the area of the rectangle is given, the following equation must be true.

Replacing  in this equation with its value stated in the first equation results in the following.

Distribute the variable into the parentheses.

Factor the polynomial.

 and  are both solutions for this equation, but  is not valid as a width for a rectangle. The width of the rectangle is  units, which is the shorter side since the length is  units longer .

The formula for the perimeter of a rectangle is:

, where represents the length and represents the width.

We know the perimeter of the rectange is  and the length is . Plugging these values into the equation, we get: