SOLUTION: you are building an addition on to your house. you only have enough money to buy 70 feet or exterior building materials. one side will be against the original house, so you only ha

Algebra ->  Sequences-and-series -> SOLUTION: you are building an addition on to your house. you only have enough money to buy 70 feet or exterior building materials. one side will be against the original house, so you only ha      Log On


   

Question 166647: you are building an addition on to your house. you only have enough money to buy 70 feet or exterior building materials. one side will be against the original house, so you only have to have materials for 3 sides. what would be the dimensions of the additon needed to give the maximim area? the is the maximum area?

thank you i really need help
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You are building an addition on to your house. you only have enough money to
buy 70 feet or exterior building materials. one side will be against the
original house, so you only have to have materials for 3 sides. what would
be the dimensions of the addition needed to give the maximum area? the is the maximum area?
:
Treat this as the 70' perimeter of three sides:
The length of one side is against the the house, therefore:
L + 2W = 70
L = (70 - 2W)
:
Find the area:
A = L * W =
Substitute (70-2W) for L
A = (70-2W)*W
A = -2W^2 + 70W
:
This is a quadratic equation, max area will be on the axis of symmetry
Find that using x = %28-b%29%2F%282%2Aa%29; in this equation a=-2; b=70
W = -70%2F%282%2A-2%29
W = %28-70%29%2F%28-4%29
W = +17.5 ft it the width for max area
:
L = 2(17.5)
L = 35 ft is the length
:
What is the maximum area?
;
35 * 17.5 = 612.5 sq/ft
:
:
You can confirm this by substituting 17.5 for W and finding the vertex:
A = -2(17.5^2) + 70(17.5)
A = -612.5 + 1225
A = + 612.5 sq ft is the vertex (max)