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# Applying the metric system to perimeter

Video transcript

The perimeter of a rectangular
fence measures 0.72 kilometers. The length of the fenced
area is 160 meters. What is its width? So we have a rectangular
fence. Let me draw it. So that is a rectangle. You can imagine we're
looking from above. This line is the top
of the fence. And if you take its perimeter,
the perimeter is the distance around the fence. If you take this distance plus
this distance plus that distance plus that distance,
it's going to be 0.72 kilometers. That's the total distance
of all of the sides. Now, the length of the fenced
area is 160 meters. Let's call this the length. So this distance right
here is 160 meters. Since it's a rectangle, that
distance over there is also going to be 160 meters, and we
need to figure out its width. They want us to figure
out the width. The width is this distance right
over here, which is also going to be this distance
right over there. Now, what is the perimeter
of the fence? The perimeter is the sum of this
length plus this length plus that length plus
that length. So the perimeter-- let me write
it in orange-- is going to be equal to w, the width,
plus 160 meters, plus the width, plus 160 meters. And let's assume
w is in meters. So we could add it all up. So if you were to add all of
these up, you'd get a certain number of meters. If you were to add all of these
up, you have a w plus a w, so you'd be 2w, plus-- 160
plus 160 is 320-- so plus 320. And this whole thing
is in meters. We're assuming that
w is in meters. Now, they also told us that the
perimeter of the fence is 0.72 kilometers. So the perimeter-- let me do it
in that same orange color. The perimeter is also equal to
0.72 kilometers, and we can abbreviate that with km. Now, if we wanted to solve an
equation, if we wanted to set this thing equal to the
perimeter they gave us, we have to make sure that the
units are the same. Here it's in meters. Here it's in kilometers. So let's convert this 0.72
kilometers to meters. And the way to do that, we want
the kilometers in the denominator so it cancels out
with the kilometers, and you want meters in the numerator. Now, how many meters
equal a kilometer? Well, it's 1,000 meters
for every 1 kilometer. 1 kilometer is 1,000 meters. Now, if you multiply these
two things, the kilometers cancel out. You're just going to be
left with the meters. And then when you multiply 0.72
times 1,000, you could just first say, OK, let's
take 72 times 1,000. 72 times 1,000 would
be 72 with three zeroes: one, two, three. And then out of the two numbers
that you're taking the product of, we have two
numbers behind the decimal: one, two. So you put two numbers behind
the decimal, one, two, right over there. So 0.72 times 1,000 is 720. And that makes sense. 0.72, it's not quite 1, but
it's getting close to 1, almost 3/4 of a whole, and this
is almost 3/4 of 1,000. So it makes sense. So the perimeter, this
information right here, 0.72 kilometers, is the same
thing as 720 meters. So if you take 2 times the width
in meters, and add that to the combined lengths-- it's
160 and 160, that's 320, and all of this is in meters-- that
is going to be equal to the total perimeter, which
is 720 meters. Now that we have the units
right, we can solve for w, and w will tell us this
width in meters. So 2w plus 320 is
equal to 720. We can subtract 320 from both
sides of this equation. Remember, an equation is saying,
that is equal to that. If we want them both always to
be equal, whatever we do to the left-hand side, we have
to do the right-hand side. So we subtract 320
from both sides. The left-hand side,
that cancels out. That's why we subtracted 320. And you just have left 2 times
the width is equal to 720 minus 320, which is 400. Now you can divide both
sides of this by 2. And then you're left with
the w is equal to 400/2, which is 200. And we said that w was
in meters, so the width is 200 meters. Let's see if it makes sense. 200 plus 200 is 400,
plus 320 is 720. So the total perimeter is 720
meters, which is the exact same thing as 0.72 kilometers.