SOLUTION: John has 1424 meters of fencing and wants to enclose a rectangular plot that borders on a lake. If he does not fence along the lake, what is the largest area that can be enclosed?
Algebra.Com
Question 1098344: John has 1424 meters of fencing and wants to enclose a rectangular plot that borders on a lake. If he does not fence along the lake, what is the largest area that can be enclosed?
My work:
I set up two equations, 1.) and 2.)
1.)
2.)
Using , I solved for L
Using I plug in the L from the above equation
Then I found the vertex using
Using 356 I plug it into the equation
This gives me the largest area = 253,472 meters squared as my final answer.
I'm just wondering if this is ok or totally off
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
It is PERFECTLY RIGHT and PERFECTLY CORRECT.
As my present/my gift to you, consider these lessons in this site
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
- A rectangle with a given perimeter which has the maximal area is a square
- A farmer planning to fence a rectangular garden to enclose the maximal area
- A farmer planning to fence a rectangular area along the river to enclose the maximal area (*)
- A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area
- Using quadratic functions to solve problems on maximizing revenue/profit
- OVERVIEW of lessons on finding the maximum/minimum of a quadratic function
The lesson marked (*) in the list has very close/similar problem.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are 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.
RELATED QUESTIONS
Farmer Ed has 4,000 meters of fencing, and wants to enclose a rectangular plot that... (answered by macston)
Farmer Ed has 900900 meters of fencing, and wants to enclose a rectangular plot... (answered by josmiceli)
Farmer Ed has 4,000 meters of fencing, and wants to enclose a rectangular plot that... (answered by macston)
Farmer Ed has 3,000 meters of​ fencing, and wants to enclose a rectangular plot that... (answered by Boreal)
You have 108 feet of fencing to enclose a rectangular plot that borders on a river. If... (answered by TimothyLamb)
The owner of a motel has 2700 m of fencing and wants to enclose a rectangular plot of... (answered by ikleyn)
A farmer with 1000 meters of fencing wants to enclose a rectangular plot that borders... (answered by KMST)
a farmer with 4000 meters of fencing wants to encloce a rectangular plot that borders on... (answered by checkley77)
A developer wants to enclose a rectangular lot that borders a city street. If the... (answered by bucky)