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.Com
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)   (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 = ; in this equation a=-2; b=70
W =
W =
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)

RELATED QUESTIONS

You have decided to update your house by laying a new wood floor in your living room.... (answered by ewatrrr)
You are building a deck and have enough lumber to make it 88 feet^2. if you want the... (answered by fractalier)
A fire is raging in an apartment house. You see kids in a window in an upstairs window. (answered by edjones)
Refining the "What-If-Analysis" to make a better Decision Support System Step 1... (answered by solver91311)
At a certain point in a large, level park, the angle of elevation to the top of an office (answered by solver91311)
The greenhouse I am building for my wife is 6 feet longer than it is wide.I only have... (answered by cristiana)
The greenhouse I am building for my wife is 6 feet longer than it is wide. I only have... (answered by Earlsdon)
You are saving to buy your first new car priced at $19,000! You have already saved... (answered by macston)
You are trying to decide if you have enough money to retire. You are expecting $1600 a... (answered by jorel555,addingup)