Question 3405: Can you help:
Sue wants to put a rectangular garden on her property using 80 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the gardens area as a function of x. Find the dimensions of the field so that its area is a maximum.
Found 2 solutions by khwang, pannalal:
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Let the three sides be y, x and y
Sum of the three sides x + 2y = 80 , so y = (80-x)/2
Area of the rectangle A = xy = x(80-x)/2 = 40x -x^2/2
By complete square A = -1/2(x^2 - 80x + (80/2)^2) + 1600/2
= -1/2(x - 40)^2 + 800
Since (x - 40)^2 >=0, -1/2(x - 40)^2 <= 0,
A = -1/2(x - 40)^2 + 800 <= 800,
when x = 40, y = (80-40)/2 = 20.
Hence, when the dimensions of the field are 20,40 and 20 meters
the max area is 800 sq. meters.
Kenny
PS. Also, try to get rid of some redunant words which are not
related to math in this question. Like :
There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle.
Answer by pannalal(9) (Show Source):
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