SOLUTION: Suppose you want to use 400 meters of fencing to surround two identical adjacent rectangular plots. Write an equation for the combined area of the plots with respect to the length

Question 551426: Suppose you want to use 400 meters of fencing to surround two identical adjacent rectangular plots. Write an equation for the combined area of the plots with respect to the length of one of the sides (x). What dimensions would produce the maximum combined area? What is that maximum combined area?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Suppose you want to use 400 meters of fencing to surround two identical adjacent rectangular plots.
Write an equation for the combined area of the plots with respect to the length of one of the sides (x).
What dimensions would produce the maximum combined area? What is that maximum combined area?
:
Let x = the width
Let L = the length
:
Two adjacent plots, therefore:
2L + 3x = 400
Arrange for substitution
2L = 400 - 3x
divide both sides by 2
L = (200-1.5x)
:
Area = x * L
Substitute (200-1.5x) for L
A = x(200-1.5x)
A quadratic equation
A = -1.5x^2 + 200x
Max area occurs at the axis of symmetry, x - -b/(2a); a=-1.5, b=200
x =
x = +66.67 meters is the width for max area
then
L = 200 - 1.5(66.67)
L = 200 - 100
L = 100 meters is the length
:
Find the max area:
100 * 66.67 = 6667 sq/meters
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