SOLUTION: you have 80 yards of fencing to enclose a rectangular region. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area?

Click here to see ALL problems on Quadratic Equations

Question 74405This question is from textbook introduction and intermediate algebra
: you have 80 yards of fencing to enclose a rectangular region. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area? This question is from textbook introduction and intermediate algebra

Answer by Cintchr(481) (Show Source):
You can put this solution on YOUR website!
With any problem like thes there are Maximums and Minimums ... and when talking fencing we have to look at Perimeter first.

P1 = 1 + 1 + 39 + 39 = 80 The Area is 1 * 39 = 39
P2 = 2 + 2 + 38 + 38 = 80 The Area is 2 * 38 = 76
P3 = 3 + 3 + 37 + 37 = 80 The Area is 3 * 37 = 111
P4 = 4 + 4 + 36 + 36 = 80 The area is 4 * 36 = 144
etc .....

Notice how the area gets larger as the shape moves from a rectangle to a square. A square will maximize the area that fencing can enclose. With a length of 80 ft, our dimentions are 20 by 20.

P20 = 20 + 20 + 20 + 20 = 80 The Area is 20 * 20 = 400