SOLUTION: Cindy wants to construct five rectangular dog training areas side by side, using a total of 600 ft of fencing. What should the overall width and length be to maximize the area of t
Algebra.Com
Question 1054244: Cindy wants to construct five rectangular dog training areas side by side, using a total of 600 ft of fencing. What should the overall width and length be to maximize the area of the five combined areas? What are the dimensions of each individual arena? What's the area of each arena?
I don't understand how to do the set up
Thanks!
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Cindy wants to construct five rectangular dog training areas side by side, using a total of 600 ft of fencing. What should the overall width and length be to maximize the area of the five combined areas? What are the dimensions of each individual arena? What's the area of each arena?
----------------------
Sketch a rectangle that is wider than high.
Sketch in 4 vertical segments to create 5 equal-areas in the rectangle.
----------
You now have 6 vertical pieces plus a base and a top.
-----------------
Let each verticle be "x".
Each horizontal piece is (600-6x)/2 = 300-3x
-----------
Area = x(300-3x) = -3x^2 + 300x
----
Max occurs when x = -b/(2a) = -300/(2(-3)) = 50
----
Dimensions of each small area::
height = x = 50 ft
width = (300-3x)/5 = (300-3*50)/5 = (300-150)/5 = 30 ft
---
Each small area = 50 by 30 = 1500 sq ft.
------------
Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the sum of the 5
sides of the 5 rectangles.
Let = the short side of
the 5 combined rectangles
----------------------------
is the "outside "
perimeter. I need to add in
for the internal sides of the 5 areas
(1)
The formula for area is:
(2)
------------------------
(1)
Plug this into (2)
(2)
(2)
This is a parabola with a positive peak
The y-value of the peak is:
ft
-------------------
(1)
(1)
(1)
(1) ft
-------------------------
The maximum area is:
ft2
------------------------
The overall dimesions are:
50 x 150
--------------------------
The dimensions of the individual areas are:
x
x
30 x 50
-------------
Hope this is understandable & I got it right!
RELATED QUESTIONS
Carl wants to construct three rectangular dog-training arenas side-by-side using a total... (answered by solver91311)
Philip wants to construct a dog pen at the back of his garage. He will use the wall of... (answered by Boreal)
problem solving using quadratic functions:
Philip wants to construct a dog pen at the (answered by solver91311)
A store wants to construct rectangular parking lot on land bordered on one side by a... (answered by checkley77)
A college is planning to construct a rectangular parking lot on land bordered on one side (answered by josmiceli)
What is the maximum amount of fencing needed to construct a rectangle enclosure... (answered by josgarithmetic,ikleyn)
What is the minimum amount of fencing needed to construct a rectangular enclosure... (answered by ankor@dixie-net.com)
A farmer has 200 feet of fencing. Using a barn as one side, the farmer wants to create a... (answered by richwmiller)
Tessa has 56 ft of fencing available to construct a fence that will divide her garden... (answered by addingup,josgarithmetic)