Question 143242
Ah...okay! <br>
So in the problem it stated that "The length is double its width."<br> 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.<br> 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.<br> 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. <br> {{{2w=L}}}<br> 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 {{{w+2L=680}}}. <br>
And here is when we insert our equation from before. (the 2w=L) So that the equation should read <br> {{{w+2(2w)=680}}}<br>
but that can be simplified, so now it can be <br> {{{w+4w=680}}} and it can still be simplified, so now it'll be <br> {{{5w=680}}}<br> 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. <br> {{{w=136}}}<br> 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 {{{1/2L=w}}} instead of {{{2w=L}}}. But that'd just be a waste of lead. So you can just use that equation from earlier (remember {{{2w=L}}}?) now just insert our answer (136) into that equation. ({{{2(136)=272}}}) And that's your Length!<br> Now, if you wanted to double check, you could use your other equation from earlier ({{{w+2L=680}}}) And insert your answers again. ({{{136+2(272)=680}}}) And simplify until it works.<br>
{{{136+544=680}}}<br>
{{{680=680}}}<br>
And there you have it!