Geometry - How to find the perimeter of a rectangle

A rectangle has an area of $96 ; cm^{2}$ . The width is four less than the length. What is the perimeter?

Explanation

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 $x^{2}-4x-96=0$ .

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 .

If the area of the rectangle is , what is the perimeter?

Explanation

In order to find the perimeter of a rectangle, you will need to know both length and width. The question, however, only provides us with the width.

Recall how to find the area of the rectangle:

$\text{Area}=\text{length}\times\text{width}$

Now, using the area and the given width, we can then find the length.

$\text{length}=\frac{\text{Area}}{\text{width}}$

Plug in the given values.

$\text{length}=\frac{600}{100}=6$

Now that we have both length and width, find the perimeter of the rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

$\text{Perimeter}=2(6+100)=2(106)=212$

A rectangle has an area of 56 square feet, and a width of 4 feet. What is the perimeter, in feet, of the rectangle?

120

Explanation

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.

One side of a rectangle is 7 inches and another is 9 inches. What is the perimeter of the rectangle in inches?

Explanation

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.

$(2\cdot 9)+(2\cdot 7)=32$

Find the perimeter of this rectangle.

Rectangle_6-24

Explanation

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.

Horton's Tile and Fixtures cuts Spanish tile in a rectangular shape that is wide and has an area of . What would be the perimeter of a cut Spanish tile?

Explanation

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

$\area=length\cdot width\315;cm^2=length\cdot15;cm\length=\frac{315;cm^2}{15;cm=21;cm}$

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

Given the rectangle in the diagram, what is the perimeter of the rectangle?

$38\ cm$

$19\ cm$

$24\ cm$

$14\ cm$

$40\ cm$

Explanation

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: