Content

• Steps

There are many ways to find an unknown size of a rectangle, and you will choose a calculation method based on the information provided. If you know the area or perimeter and the length of one side of the rectangle (or the relationship between the length and the width), you can find the length of the other side. You can use the properties of a rectangle as the method of calculating the length or width.

Steps

Method 1 of 4: Use area and length

1. 

   Set up the formula for the area of ​​a rectangle. The formula is, where is the area, is the length, and is the width of the rectangle.
   • You will only be able to use this method if the problem is to provide the area and length of the rectangle.
   • The formula for the area can also be written as, where is the height of the rectangle and is used instead of the length. These two quantities represent the same measure.

2. 

   
   
   Plug the values ​​for area and length into the formula. Remember to replace values ​​with the correct variables.
   • For example, if you want 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:
     

3. 

   Solve search. You must divide the two sides of the equation by the length.
   • For example, in the equation, you would divide each side by 8.
     
     
     

4. 

   
   
   Write your final answer. Don't forget to write the unit of length.
   • For example, for a rectangle with area and length, the width would be.
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Method 2 of 4: Use perimeter and length

1. 

   Set up the formula for the perimeter of the rectangle. The formula is, where the perimeter, is the length, and the width of the rectangle.
   • This method will only work if you are given perimeter and rectangular length in the problem.
   • The perimeter formula can also be written as, where is the height of the rectangle and is used instead of the length. Variables and only one measure, by the distributive nature, both produce the same results even though written differently.

2. 

   
   
   Plug the values ​​for perimeter and length into the formula. Remember to replace values ​​with the correct variables.
   • For example, if you want to find the width of a rectangle with a circumference of 22 centimeters and a length of 8 centimeters, your formula will look like this:
     
     

3. 

   Solve search. You must subtract 2 sides of the equation by the length and then divide by 2.
   • For example, in the equation, you would subtract both sides of the equation by 16, and then divide the sides by 2.
     
     
     
     

4. 

   Write your final answer. Don't forget to write the unit of length.
   • For example, for a rectangle with perimeter and length, the width would be.
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Method 3 of 4: Use diagonal and length

1. 

   Set up the formula for the diagonal of the rectangle. The formula is, where the length of the diagonal is the length, and the width of the rectangle.
   • This method will only work if you are given the diagonal length and one side of the rectangle.
   • The formula for the diagonal can also be written as, where is the height of the rectangle and is used instead of the length. Variables and only one measure.

2. 

   Plug the diagonal and side lengths into the formula. Remember to replace the values ​​with the correct variables.
   • For example, if you want to find the width of a rectangle whose diagonal length is 5 centimeters, and one side is 4 centimeters, your formula will look like this:

3. 

   Calculate the square of the two sides of the equation. You must squared to get rid of the square root, making it easier to calculate the variable of the width.
   • For example:
     
     
     

4. 

   Transform the equation so that one side has only variables. You must subtract the two sides of the equation from the squared length.
   • For example, in the equation, you would subtract both sides of the equation for 16.
     
     

5. 

   Solve search. To solve the equation you must calculate the square root of the two sides.
   • For example:
     
     

6. 

   Write your final answer. Don't forget to write the unit of length.
   • For example, for a rectangle that is diagonal length and one side length is, the width would be.
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Method 4 of 4: Use the area or perimeter and the relationship between the two sides

1. 

   Set up the formula for the area or perimeter of a rectangle. You will choose the recipe to use according to the data provided by the topic. If the problem provides an area, make a formula for the area. If the problem provides perimeter, make a formula for perimeter.
   • If you don't know the area or the perimeter, or don't know the relationship between the length and the width, you can't use this method.
   • The formula for the area is.
   • The formula for perimeter is.
   • For example, maybe you know that the area of ​​a rectangle is 24 square centimeters, so you will formulate the formula for the area of ​​a rectangle.

2. 

   Write an expression that describes the relationship between length and width. Write expressions in a form that is only on one side of the equal sign.
   • The problem can tell how many times one side is longer than the other, or how many units longer one side is from the other.
   • For example, it is said that the length is 5 centimeters longer than the width. Then the length expression is.

3. 

   Substitute the length expression for the variable in your formula for area (or perimeter). Now the formula has only one variable, meaning you can solve for the width.
   • For example, if you know the area is 24 square centimeters and, the formula will look like this:
     
     

4. 

   Simple equation. The simplified equation may have a different form depending on the relationship between width and length, and whether the problem provides area or perimeter. Find a way to set up an equation so that you can solve it most easily.
   • For example, you can simplify the equation into.

5. 

   Solve search. How to solve it depends on how simple the equation is. Use basic principles of algebra and geometry to solve equations.
   • You may have to add or divide, analyze a quadratic equation into a factor, or use a quadratic formula to solve an equation.
   • For example, which can be factorized as follows:
     
     
     Then you find two solutions of: hay. Since the rectangular width cannot have negative values, you remove the -8 root. So the answer is.
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