Two rectangles are similar if and only if their sides are in proportion. Specifically, 

Rectangle  Rectangle 

if 

Since  is located at the point , it follows that  and . Since  is located at the point , it follows that  and . Substituting in the aforementioned proportion statement, we get

.

Reducing to lowest terms, this is

.

This is false, so Rectangle  Rectangle .

Comparing the sides  and , we see that is  the length of , as shown here:

.

Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of  to  is also , and we can calculate the length of  by setting up and solving a proportion:

.

Hence, the length of the side  is  units.

The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:

The perimeter is 38 cm.

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width).  Multiply both the height and width by two and add the results.

For a rectangle, area is  and perimeter is , where is the length and is the width.

Let = length and = width.

The area equation to solve becomes , or .

To factor, find two numbers the sum to -4 and multiply to -96.  -12 and 8 will work:

x² + 8x - 12x - 96 = 0

x(x + 8) - 12(x + 8) = 0

(x - 12)(x + 8) = 0

Set each factor equal to zero and solve:

or .

Therefore the length is  and the width is , giving a perimeter of .

Convert the dimensions from yards to feet by multiplying by 3: This makes the dimensions 600 feet and 1,200 feet. The perimeter of this farm is therefore

.

Multiply this by the cost of the fence per foot:

To find the perimeter of any rectangle, add all of the sides up:

20 + 20 + 12 + 12 = 64 inches

You could use this formula as well:

, where P = perimeter,  l = length, w = width

This formula comes from the fact that there are 2 lengths and 2 widths in every rectangle.

Remember, the perimeter of the rectangle is the sum of all four sides:

It is obvious from the figure that A=6 and B=24.

Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.

The area of a rectangle is the width times the height, and we are told that in this rectangle the width is two times the height.

Therefore, .

Plug in the value of the area:

Solve for  to find a width of 4 inches. Using our formula above, the height must be 8 inches.  We then add all the sides of the rectangle together to find the perimeter: