How Do You Use Algebra to Find the Dimensions of a Rectangle When the Perimeter Is Given?

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In algebra, you use some amount of known information to solve for an unknown variable. If you are given the perimeter of a rectangle, you might be asked to solve for its dimensions.

  1. Figure out what you already know

    The formula for the perimeter of a rectangle is 2(b + h), where b is the base and h is the height. You might also see length or width used to describe the dimensions. This means that your given perimeter, or P, is equal to twice the sum of the base and the height. So if the perimeter is 20, then the base plus the height equals the perimeter divided by two, which is 10. For this to be true, the rectangle could be 5 by 5, 3 by 7 or 1 by 9, among many other possibilities. To determine the dimensions for certain, you need additional information, such as the area of the rectangle or the ratio of the sides.

  2. Use substitution to solve for one variable

    If you were told that the perimeter is 20 and the base is four times bigger than the height, you would have two equations: b + h = 10 and b = 4h. Substitute one variable for the other, since you know the how they relate to one another: (4h) + h = 10, so 5h = 10 and h = 2.

  3. Use the known variable to solve for the unknown

    The same principle of substitution works for finding the second variable. In this example, since h = 2 and b = 4h, then b = 8.

  4. Check your answer

    If the perimeter is 20, then twice the sum of the base and the height must also equal 20. For instance, 2(2 + 8) = 2(10) = 20.