# How to Find the Width of a Rectangle

Co-authored by wikiHow Staff

Updated: January 23, 2020

There are numerous ways to find a missing dimension of a rectangle, and the method you use will depend on what information you already have. As long as you know the area or perimeter, as well as the length of one side of the rectangle (or the relationship between the length and width), you can find a missing dimension. The properties of a rectangle are such that you can use these methods for finding the width or length.

### Method 1 of 4: Using Area and Length

1. 1
Set up the formula for area of a rectangle. The formula is ${\displaystyle A=(l)(w)}$, where ${\displaystyle A}$ equals the area of the rectangle, ${\displaystyle l}$ equals the length of the rectangle, and ${\displaystyle w}$ equals the width of the rectangle.[1]
• This method will only work if you are given the area and length of the rectangle.
• You might also see the formula written as ${\displaystyle A=(h)(w)}$, where ${\displaystyle h}$ equals the height of the rectangle and is used instead of length.[2] These two terms refer to the same measurement.
2. 2
Plug the values for area and length into the formula. Make sure you substitute for the correct variables.
• For example, if you are trying to find the width of a rectangle that has an area of 24 square centimeters, and a length of 8 centimeters, your formula will look like this:
${\displaystyle 24=8w}$
3. 3
Solve for . To do this, you need to divide each side of the equation by the length.
• For example, in the equation ${\displaystyle 24=8w}$, you would divide each side by 8.
${\displaystyle 24=8w}$
${\displaystyle {\frac {24}{8}}={\frac {8w}{8}}}$
${\displaystyle 3=w}$
4. 4
Write your final answer. Don’t forget to include the unit of measurement.
• For example, for a rectangle with an area of ${\displaystyle 24cm^{2}}$ and a length of ${\displaystyle 8cm}$, the width would be ${\displaystyle 3cm}$.

### Method 2 of 4: Using Perimeter and Length

1. 1
Set up the formula for perimeter of a rectangle. The formula is ${\displaystyle P=2l+2w}$, where ${\displaystyle P}$ equals the perimeter of the rectangle, ${\displaystyle l}$ equals the length of the rectangle, and ${\displaystyle w}$ equals the width of the rectangle.[3]
• This method will only work if you are given the perimeter and length of the rectangle.
• You might also see the formula written as ${\displaystyle P=2(w+h)}$, where ${\displaystyle h}$ equals the height of the rectangle and is used instead of length.[4] The variables ${\displaystyle l}$ and ${\displaystyle h}$ refer to the same measurement, and the distributive property dictates that these two formulas, although arranged differently, will give you the same result.
2. 2
Plug the values for perimeter and length into the formula. Make sure you substitute for the correct variables.
• For example, if you are trying to find the width of a rectangle that has a perimeter of 22 centimeters, and a length of 8 centimeters, your formula will look like this:
${\displaystyle 22=2(8)+2w}$
${\displaystyle 22=16+2w}$
3. 3
Solve for . To do this, you need to subtract the length from each side of the equation, then divide by 2.
• For example, in the equation ${\displaystyle 22=16+2w}$, you would subtract 16 from each side, then divide by 2.
${\displaystyle 22=16+2w}$
${\displaystyle 6=2w}$
${\displaystyle {\frac {6}{2}}={\frac {2w}{2}}}$
${\displaystyle 3=w}$
4. 4
Write your final answer. Don’t forget to include the unit of measurement.
• For example, for a rectangle with a perimeter of ${\displaystyle 22cm}$ and a length of ${\displaystyle 8cm}$, the width would be ${\displaystyle 3cm}$.

### Method 3 of 4: Using the Diagonal and Length

1. 1
Set up the formula for the diagonal of a rectangle. The formula is ${\displaystyle D={\sqrt {w^{2}+l^{2}}}}$, where ${\displaystyle D}$ equals the length of the rectangle’s diagonal, ${\displaystyle l}$ equals the length of the rectangle, and ${\displaystyle w}$ equals the width of the rectangle.[5]
• This method will only work if you are given the length of the diagonal and the length of the side of the rectangle.
• You might also see the formula written as ${\displaystyle D={\sqrt {w^{2}+h^{2}}}}$, where ${\displaystyle h}$ equals the height of the rectangle and is used instead of length.[6] The variables ${\displaystyle l}$ and ${\displaystyle h}$ refer to the same measurement.
2. 2
Plug the values for the diagonal and side length into the formula. Make sure you substitute for the correct variables.
• For example, if you are trying to find the width of a rectangle that has a diagonal length of 5 centimeters, and a side length of 4 centimeters, your formula will look like this: ${\displaystyle 5={\sqrt {w^{2}+4^{2}}}}$
3. 3
Square both sides of the formula. You need to do this to get rid of the square root sign, which makes isolating the width variable easier.
• For example:
${\displaystyle 5={\sqrt {w^{2}+4^{2}}}}$
${\displaystyle 5^{2}=w^{2}+4^{2}}$
${\displaystyle 25=w^{2}+16}$
4. 4
Isolate the variable. To do this, you need to subtract the squared length from each side of the equation.
• For example, in the equation ${\displaystyle 25=16+w^{2}}$, you would subtract 16 from each side.
${\displaystyle 25=16+w^{2}}$
${\displaystyle 9=w^{2}}$
5. 5
Solve for . To do this, you need to find the square root of each side of the equation.
• For example:
${\displaystyle {\sqrt {9}}={\sqrt {w^{2}}}}$
${\displaystyle 3=w}$
6. 6
Write your final answer. Don’t forget to include the unit of measurement.
• For example, for a rectangle with a diagonal length of ${\displaystyle 5cm}$ and a side length of ${\displaystyle 4cm}$, the width would be ${\displaystyle 3cm}$.

### Method 4 of 4: Using Area or Perimeter and Relative Length

1. 1
Set up the formula for area or perimeter of a rectangle. Which formula you use will depend on which measurement you are given. If you are given the area, set up the area formula. If you are given the perimeter, set up the perimeter formula.
• If you do not know the area or the perimeter, or the relationship between the length and the width, you cannot use this method.
• The formula for area is ${\displaystyle A=(l)(w)}$.
• The formula for perimeter is ${\displaystyle P=2l+2w}$.
• For example, you might know that the area of a rectangle is 24 square centimeters, so you would set up the formula for area of a rectangle.
2. 2
Write the expression that describes the relationship between the length and the width. Write your expression in terms of what ${\displaystyle l}$ equals.
• The relationship might be given by stating how many times bigger one side is than the other, or how many units more or less it is.
• For example, you might know that the length is five centimeters longer than the width. Your expression for the length is then ${\displaystyle l=w+5}$.
3. 3
Replace the variable in your area (or perimeter) formula with the expression for length. Your formula should now only contain the variable ${\displaystyle w}$, which means you can solve for the width.
• For example, if you know that area is 24 square centimeters, and that ${\displaystyle l=w+5}$, your formula will look like this:
${\displaystyle A=(l)(w)}$
${\displaystyle 24=(w+5)(w)}$
4. 4
Simplify the equation. Your simplified equation might take on various forms, depending on the relationship between the length and the width, and depending on whether you are working with area or perimeter.[7] Think about setting up an equation that allows you to solve for ${\displaystyle w}$ in the simplest way.
• For example, you can simplify ${\displaystyle 24=(w+5)(w)}$ to ${\displaystyle 0=w^{2}+5w-24}$.
5. 5
Solve for . Again, how you solve for ${\displaystyle w}$ will depend on your simplified equation. Use the basic rules of algebra and geometry to solve.
• You might need to use addition or division to solve, or you might need to factor a quadratic equation or use the quadratic formula to solve.[8]
• For example, ${\displaystyle 0=w^{2}+5w-24}$ can be factored as follows:
${\displaystyle 0=w^{2}+5w-24}$
${\displaystyle 0=(w+8)(w-3)}$
You will then have two possible solutions for ${\displaystyle w}$: ${\displaystyle w=3}$ or ${\displaystyle w=-8}$. Since a rectangle cannot have a negative width, you can eliminate -8. So your solution is ${\displaystyle w=3}$.[9]

## Community Q&A

Search
• Question
How would I find width when I've been given volume, height, and length?
Blankless X
You divide the volume by the height and the length. You could multiply the height and the length with each other first before dividing. W = V / (H*L).
• Question
The length of a rectangle field is twice its breadth. Its perimeter is 400m. How do I find the length and breadth?
Donagan
Let B equal the breadth. Then 2B equals the length. Write an equation in B, stating that the perimeter is equal to twice the breadth plus twice the length. Solve for B.
• Question
How do I find the area of a rectangle if width and perimeter are given?
Donagan
Double the width, and subtract that from the perimeter. Then divide that number by two, which gives you the length of the rectangle. Then, multiply the result by the width to get the area.
• Question
How do I find the dimensions of a rectangle if the perimeter is 33 and the length equals twice the width?
Donagan
The length (l) is twice the width (w), so l = 2w. The perimeter, or twice the length plus twice the width, is 33, so 2(2w) + 2w = 33. That means 6w = 33; w = 5½, and 2w = l = 11.
• Question
Area = 40" and perimeter = 28"; how do I find side lengths of a rectangle?
Donagan
Let x and y be the dimensions of the rectangle. Then xy = 40, and 2x + 2y = 28. From the first equation, x = 40/y. Substituting that value of x into the second equation, 2(40/y) + 2y = (80/y) + 2y = 28. Multiply both sides of this equation by y to get rid of the denominator: 80 + 2y² = 28y. Divide by 2 to simplify: 40 + y² = 14y. Subtract 14y from both sides to get zero on one side, and re-arrange slightly: y² - 14y + 40 = 0. Factor the left side: (y - 10)(y - 4) = 0. Set each factor equal to zero to solve for y: y = 4, 10. That means that one side of the rectangle is 4 inches in length, and the other side is 10 inches.
• Question
The area is 77 m^2, but all I know about the length is that it's 4 m longer than the width. How do I find the width?
Donagan
Set up an equation in which the width (w) is multiplied by four-more-than-the-width (w + 4) to equal 77. Then solve for the width.
• Question
How do I find side lengths of a rectangle if only area and perimeter are given?
Donagan
Let l and w be the length and width respectively. Set up equations in l and w for the perimeter and the area. Use either equation to solve for l in terms of w, or vice versa, then substitute that value of l into the other equation. That will give you the value of w. Use it in either equation to find the value of l.
• Question
One side of a square chessboard is 75 cm; how would I find the area of the board?
Donagan
Square the side.
• Question
If only area is given, how do I find length and height?
Donagan
You cannot find length and width if all you're given is area.
• Question
If I am given the area and width, how do I get the length?
Donagan
Divide area by width.
• How can I find the breadth of a rectangle if I'm given its perimeter and length?
• How can I calculate the length and width of a rectangle if I am given the area?
• How do I find the width of a rectangle if I know the area and length?
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Co-Authored By:
wikiHow Staff Editor
This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Together, they cited information from 9 references.
Co-authors: 12
Updated: January 23, 2020
Views: 396,068
Categories: Geometry
Article SummaryX

To find the width of a rectangle, use the formula: area = length × width. Just plug the area and length of the rectangle into the formula and solve for the width. If you don't have the area, you can use the rectangle's perimeter instead. In that case, you would use the formula: perimeter = 2 × length plus 2 × width. Plug the perimeter and the length into the formula and solve for the width. To learn how to find the width of a rectangle using the diagonal and the length, scroll down!
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