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>> So here's a word problem
involving a rectangle.

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We know that the perimeter of a rectangle
is 100 yards, and we want to find

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out what the dimensions of that rectangle are
if the length if 20 yards more than the width.

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So, let's see, perimeter, what does that mean?

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Well, perimeter is just the
distance you would walk

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if you walked all the way around that rectangle.

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So we could write down perimeter
equals distance around the shape.

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And this is true not just for
rectangle but for other shapes as well.

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So let's see what we've got here.

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Let's draw a rectangle and go
ahead and label its dimensions.

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And when they say dimensions
they mean length and width.

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So let's call that length L, and let's call the
width W. And then on my picture here I can draw

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in the lengths and draw in the widths.

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So let's think about this.

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We know the perimeter, and I'll call it P,

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is equal to what you get if
you add up all the sides.

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So in this case that would be L plus W plus L
plus W. And if we simplify the right hand side

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of that equation we get P equals 2L plus 2W.

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And this is a formula that you can use
anytime you're dealing with the perimeter

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of a rectangle, P equals
2 lengths plus 2 widths.

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So now let's see how this
applies to this problem.

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Well, we know that the length
is 20 yards more than the width.

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So really if we knew what the width
was we could figure out the length.

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It wouldn't be too bad.

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So I'm going to go back and erase those
Ls and change them to -- well, let's see.

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The length is 20 yards more than the width,
so how about W plus 20 for the length.

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So that other wide is W plus 20 as well.

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So the width is called W and the length is now
called W plus 20 because of the relationship

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that we're given in this problem.

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Okay, so let's go ahead and see how
we can put that into our equation.

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We've got 100 for the perimeter that
was given in the problem equals 2 times,

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now instead of L I'm going to put W plus 20.

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And then don't forget your plus 2W at the end.

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So now it's just a matter of
solving a linear equation.

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This shouldn't be too bad.

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On the right hand side I'm going to go ahead
and distribute my 2 so I get 2W plus 40.

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Do not lose that plus 2W at the end.

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It's important.

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I'm still simplifying.

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On that right hand side I have like terms.

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So I'm going to go ahead and combine
the 2W and the 2W to get 4W plus 40.

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So now let's see, at this point I
can't simplify either side any further.

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So I'm going to go ahead and
subtract 40 from each side.

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That will leave me with 60 equals 4W.

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And if I want to get that W by itself it
is attached to the 4 by multiplication.

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So I'm going to divide both
sides by 4 and I get 15 for W.

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So what this means is the width
of that rectangle is 15 yards.

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And now if the width is 15 let's
see what that means for the length.

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Well, if we put 15 for the W
and then we add 20 we get 35.

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So the length is going to be 35 yards.

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And that's it.