SOLUTION: A rectangular field is to be enclosed by 440 feet of fence. What is the length of the field (in feet) if the area is a maximum?
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Question 1181394: A rectangular field is to be enclosed by 440 feet of fence. What is the length of the field (in feet) if the area is a maximum?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
A rectangle with fixed perimeter has maximum area when the rectangle is a square.
Given 440 feet of fencing, the maximum area is when the length and width are both 440/4=110 feet.
Here is a quick way to show this algebraically....
The perimeter is 440 feet, so length plus width is 220 feet.
To make the sum of length and width equal to 220, let the length be 110+x and the width be 110-x. Then the area is length times width: (110+x)(110-x)=12100-x^2.
x^2 is always 0 or positive; so the maximum area is when x is 0, making the length and width both 110 feet.
Answer by ikleyn(52831) (Show Source): You can put this solution on YOUR website!
.
For a rectangle with the given fixed perimeter, the area is maximum when the rectangle is a square.
So, with the perimeter of 440 feet and with maximum area, the rectangle is a square
with the side of 440/4 = 110 ft. ANSWER
Solved.
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See the lessons
- 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
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 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.
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