SOLUTION: A farmer has 680 feet of fencing to enclose a pasture. Because a river runs along one side, fencing will be needed only on three sides. Find the dimensions of the pasture if its le

Question 143242: A farmer has 680 feet of fencing to enclose a pasture. Because a river runs along one side, fencing will be needed only on three sides. Find the dimensions of the pasture if its length is double its width.
Answer by zephyr(9) (Show Source): You can put this solution on YOUR website!
Ah...okay!

So in the problem it stated that "The length is double its width."
That means if you had enough fence pieces to make 2 widths, then it'd be the same amount of pieces to make one length.
Still confusing? Let's say, that the width was 5 and the length was 10 (in this problem) If you had the pieces for 2 widths (5+5) it'd equal the side of a length (10). But that's just an example, now back to the problem.
So since we're going to substitute in this problem you'd need to put that statement ("the length is double its width") into a mathematical equation. Like this.

Okay. So in a rectangle, you have 2 widths, and 2 lengths, right? But since you have the river, there's only 1 width, and 2 lengths. So the equation you should have right now is .

And here is when we insert our equation from before. (the 2w=L) So that the equation should read

but that can be simplified, so now it can be
and it can still be simplified, so now it'll be

And now, to figure out the number of feet of fencing for a single width (remember, we just need one width), we divide by 5.

There! But now we have to figure out the length...if you wanted to, you could do this whole thing over again, and just use instead of . But that'd just be a waste of lead. So you can just use that equation from earlier (remember ?) now just insert our answer (136) into that equation. () And that's your Length!
Now, if you wanted to double check, you could use your other equation from earlier () And insert your answers again. () And simplify until it works.

And there you have it!
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