SOLUTION: Not sure how to go about the question, simultaneous equations? The question is as follows: A farmer has a straight, fenced road along the boundary of his property. He wises to fe

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Not sure how to go about the question, simultaneous equations? The question is as follows: A farmer has a straight, fenced road along the boundary of his property. He wises to fe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1028745: Not sure how to go about the question, simultaneous equations?
The question is as follows:
A farmer has a straight, fenced road along the boundary of his property. He wises to fence an enclosure and has enough materials to erect 500m of fence. What would the dimensions to enclose the largest possible rectangular area, assuming that he uses the existing boundary fence as one of the sides?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So it's a 3 sided rectangle that he needs to build using 500m of fencing.
The area is,
A=L%2AW
The perimeter of fencing used is,
P=500
2L%2BW=500
So you can then make area a function of one variable,
W=500-2L
Substituting,
A=L%28500-2L%29
A=-2L%5E2%2B500L
To find the maximum, convert to vertex form:
A=-2%28L%5E2-250L%29
A=-2%28L%5E2-250L%2B125%5E2%29%2B2%28125%29%5E2
A=-2%28L-125%29%5E2%2B31250
So the maximum area of 31250m%5E2 occurs when L=125m
Then,
W=500-2%28125%29
W=500-250
W=250m