# 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 â?" 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.

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#### 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.

Algebra: Word Problems on Fencing

1)A rancher is going to construct a new rectangular pen for his emu farm. If he has 2600 feet of fencing, what is the maximum area of the pen?

____ft^2

2)A farmer is fencing a rectangular pen for his sheep using the straight portion of a river as one side of the rectangle. If the farmer has 1200 feet of fencing, find the dimensions of the rectangle that gives the maximum area of the pen.

shorter side:____ft

longer side:____ft

3)A baseball is hit straight upwards with an initial velocity of 92 feet per second and leaves the bat at an initial height of 4 feet. Write a formula, s(t), that models the height of the baseball after t seconds.

s(t)=

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