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Applying the metric system to perimeter

Created by Sal Khan and Monterey Institute for Technology and Education.
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.