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# Finding width from perimeter and length

Created by Sal Khan.

Video transcript

Mike built a rectangular dog
pen that is 21 feet long, and it has a
perimeter of 78 feet. What is the width
of Mike's dog pen? So let's try to
draw this dog pen. So it's going to
have some width, and I'll just label
that as the width. And it's going to have
a length of 21 feet. So this distance right over
here is going to be 21, and of course, this is as well. It's a rectangle,
so this is also going to be a distance of 21. And of course, this
distance down here is also going to be the width. Now, how do you calculate
the perimeter of this? They tell us that the
perimeter is 78 feet, but how do we calculate
the perimeter using this information? Well, the perimeter
is just the sum of these two widths
and these two lengths. So the perimeter is going to
be the width plus the width plus the two lengths,
plus 21 plus 21. This will give us
the distance if we go around this
rectangular dog pen. And they tell us that this thing
needs to be equal to 78 feet. Let me do the same color. Now, we could simplify
this expression on the left hand
side a little bit. We know that the width plus the
width plus the sum of the two lengths-- which are
both the same-- plus 42 is going to equal 78. So what must the width
plus the width be equal to? So, I have something--
I have this thing plus 42 is equal to 78. So if I have something
plus 42 is equal to 78, that means that this
something must be 78 minus 42. So let's write that down. Width plus width is going
to be equal to 78 minus 42, which is-- I'll do it in a
new color-- 78 minus 42 is 36. And you can verify this. If this thing right over
here is equal to 36, if the sum of my two
widths-- or essentially this is 2 times the width. If 2 times the width is 36,
then width plus width is 36. Then this right over here is 36. 36 plus 42 is
indeed equal to 78. So we figure out a width so that
if I add the width to itself, I get 36, because when we
add those two, you get 36, plus 21 plus 21 is equal to 78. So what number plus itself
is going to be equal to 36? Another way to rewrite this
is a number plus itself is the same thing as
2 times that number. So 2 times the width is
going to be equal to 36. And later on when we learn
algebra in a little bit more detail, you'll see that
essentially what we're doing is actually algebra, but it
just comes out of common sense, out of logic. So if I say 2 times some
value is equal to 36, what is that value going to be? Well, 2 times 18 is 36, so
the width is equal to 18. And you might say well,
how did I figure out that the width is equal to 18? Well, there's a couple of
ways to think about it. If 2 times the width
is equal to 36, then the width must be
equal to 36 divided by 2, must be equal to 36 over 2,
which would also get you 18. So there's a lot of
ways to think about it, and later on when we learn
algebra in a little bit more details, things like this
will seem even more obvious. But I just wanted to show
you that you can actually reason this through just with
what we know about perimeter.