# Rectangular Perimeter & Area Problem

Given, this partial equation, how do I complete it?

Finding the width I used this equation - L= 2W + 2

I know my length is 10 feet. 10 = 2W + 2

10 -2 ft = 2W +2 - 2

8 = 2W

8/2 = 2W/2

4 = W

Questions:

Define the shape of the rectangular area by establishing a relationship between the length and width of the rectangle. For example, L = 2W + 5, or W = 3L รข?" 4. Be sure to include the appropriate units (inches, feet, yards, miles, or meters).

Using the fact that A = LW, together with the relationship defined in step 2, eliminate one of the variables to set up a quadratic equation.

Solve the quadratic equation using any of the techniques learned in this unit. The solution(s) will be one of the dimensions; use step 2 to find the other.

Now determine the perimeter so that you will know how much fencing to buy.

Summarize your findings.

#### Solution Preview

Repeating the given information:

L= 2W + 2

L=10

10 = 2W + 2

10 -2 ft = 2W +2 - 2

8 = 2W

8/2 = 2W/2

4 = W

A=L*W

So:

A = 2L + ...

#### Solution Summary

This solution shows how to solve a classic problem involving a fixed amount of fence to be used to enclose three sides of a rectangle with the fourth side closed by the side of a building. The problem involves relating perimeter and area to each other and solving for unknown dimensions. This is a classic algebra problem required of almost all second year high school or college level algebra courses.