How to Set Up an Equation for the Perimeter Involving Only "L" for the Length of the Rectangle

A square is differentiated from a rectangle by having all sides equal in length.

Problems involving rectangles are a useful tool for educators teaching the basics of algebra. A rectangle is a simple geometric figure with four sides where the opposite sides are parallel and equal in length and where all four internal angles are ninety degrees. The perimeter of a rectangle is the distance around its exterior. You can summarize a rectangle's perimeter as twice its length plus twice its height. You can find an equation for this perimeter using a variable "L" for the length so long as you know the ratio of height to length for the rectangle.

Things You'll Need

• Calculator

Instructions

1. Set the length of the rectangle equal to L.

2. Describe the height of the rectangle in terms of L. To do so, multiply L by the given ratio of the height to the length. For example, if you know the rectangle's height is one third of its length, the height is 1/3 x L or L/3.

3. Calculate the perimeter of the rectangle as twice the length plus twice the height. In the case of the example, the perimeter (P) would be found according to the calculation P = 2 x L + 2 x L/3.

4. Simplify the equation for the perimeter by adding together all the terms containing L. You now have a single equation for the perimeter in terms of only L. The equation for the example would simplify to P = 2L + 2/3L or P = 8/3L.

Tips & Warnings

• Once you have derived the perimeter equation, you can find the perimeter for any value of L by substituting that value for L in the equation.

References

• Oklahoma State University; Geometry: Basic Ideas: Why is a Square Also a Rectangle?; B. Yoder
• Diablo Valley College; Free Pre-Algebra; Lesson 3: Perimeter and Area; C. Wilcox; 2010

Resources

• Arkansas Tech University: Basic Geometric Shapes and Figures