SOLUTION: I am having problems with writing a function for a word problem in college algebra. The word problem is as follows: You want to enclose a rectagle for your dog. You have 84 feet

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Question 81400This question is from textbook College Algebra Graphs and Models
: I am having problems with writing a function for a word problem in college algebra. The word problem is as follows:
You want to enclose a rectagle for your dog. You have 84 feet of fencing. If the fence is x feet long, express the area as a function of the legnth.
Thank you This question is from textbook College Algebra Graphs and Models

Answer by SMM52091(3) About Me  (Show Source):
You can put this solution on YOUR website!
This one isnt too hard when you think about it. Let x be length. Perimeter is 2x + 2(width), so put it in terms of length so length will not eventually interfere with the function.
P+=+2x+%2B+2%28width%29
P+-+2x+=+2%28width%29
%28P+-+2x%29%2F%282%29+=+width
So now we can start to make the function. Area equals length times width, and we have length and width in terms of length, so the function can be made.
f%28x%29+=+%28length%29%28width%29
f%28x%29+=+x+%2A+%28P+-+2x%29%2F%282%29
f%28x%29+=+x+%2884+-+2x%29%2F%282%29 You have 84 feet of fencing to use, so that will be the perimeter.
f%28x%29+=+%2884x+-+2x%5E2%29%2F%282%29
f%28x%29+=+42x+-+x%5E2
Whenever you have x amount of length, you can plug it into the function to get the area. Hope that helps