SOLUTION: A rancher is building a pen using 150 feet of fencing. The pen will be enclosed on 3 sides, with the fourth side shared by an already existing pen. What is the function of the area

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rancher is building a pen using 150 feet of fencing. The pen will be enclosed on 3 sides, with the fourth side shared by an already existing pen. What is the function of the area      Log On


   

Question 1107907: A rancher is building a pen using 150 feet of fencing. The pen will be enclosed on 3 sides, with the fourth side shared by an already existing pen. What is the function of the area of the new pen?
Found 2 solutions by JThomson, ikleyn:
Answer by JThomson(12) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming the pen has one of its lengths shared be existing pen then;

2B + L = perimeter

2B + L = 150

But L=150-2B or B = 1/2(150-L)

So Area of the pen is;

A = B(150-2B) or 1/2(150L-L^2)

= 150B-2B^2 where L and B are the Length and

breadth respectively.

Note that Area (A) could also be 1/2(150B-B^2)
when one of the widths is shared by a pen in
which case 2L+B=150

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Very popular problem connected with it is to find the maximum area given the fixed total length of three sides of a rectangular pen.

For the solution of such a problem see the lesson
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.