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周長與單位轉換 (英) : 周長與單位轉換
- The perimeter of a rectangular fence measures 0.72 kilometers. The length of the fenced area is
- 160 meters. What is its width? Now the first thing that jumps out is that they're giving us different units.
- They're giving us the perimeter in terms of kilometers and the length in terms of meters.
- I am assuming that they want the width in meters because that's what they're giving us the length in.
- Convert the perimeter into meters. So we have the perimeter P is equal to 0.72 kilometers which I'll write km for short. Kilometers.
- 1000 meters. That's what the prefix "kilo" means.
- And so we can say that for every 1 kilometer we have a 1000 meters.
- And you might say so how do you know to multiply it by a 1000 instead of divide by a 1000?
- One way to think about it and this is probably the best way to think about it is
- a kilometer is a huge bunch of meters, its actually 1000 meters. So if I am converting kilometers into meters
- I should have a much larger number whatever my number is in kilometers it should be a much larger number in meters.
- And also if you care about Dimensional Analysis, the dimensions cancel out here too. We have km in the numerator, km in the denominator.
- So you multiply it, you have 0.72 times a 1000 m and to multiply anything times a 1000 or
- any power of 10 if I multiply it by 10 I'll move the decimal to the right one space
- that would be multiplying it by 10 , it would be 7.2,
- multiplying it by a 100 would give us 72.
- If we are multiplying by a 1000 that would give us 720.
- So this is going to be equal to 720 m. So that is the perimeter.
- Now let's remind ourselves what the perimeter even is then hopefully we can figure out the width.
- And they tell us that the length is 160 m. So let's say that that's this dimension over here.
- The length (l) is 160 m. Its a rectangle so these sides are both the same length.
- And our width is what we need to solve for so that's our width (w) and this is also our width.
- And the perimeter is the measure going around it. So the perimeter is going to be
- this length plus this width plus that same length again plus that width over there.
- Or the perimeter (P) is equal to the length (l) plus the width (w) plus the length (l) plus the width (w)
- We know what the length is so then the perimeter would be equal to
- 160 m plus w plus 160 m plus w. And then we know what the perimeter is. That's actually 720 m.
- So 720 m is equal to 160 m plus w plus 160 m plus w. Now there's a bunch of different ways to solve for w.
- One way is to just add the width plus the length once, that's going to add up to half of the perimeter.
- So if I just go half way around the rectangle that's going to add up to half the perimeter.
- So w plus 160 m should be equal to one half of the perimeter which is one half times 720 m.
- Or w plus 160 m is equal to 720 divided by 2 which is 360 m. And so now you have w plus 160 m is 360 m.
- So we could now subtract 160 from both sides to solve for it. Something plus 160 is 360,
- you could in your head say, well, that something must be 200. 200 plus 160 is 360.
- The width (w) is 200 m. Or if you want to do it a little bit more formally you subtract 160 m
- from both sides of this equation and you are left with the width (w) is equal to 200 m.
- We've solved the problem. The other way is you could actually go straight from this equation.
- So we get 720 is 160 plus 160 (320) and width (w) plus width (w) or 2 times the width (2w).
- Anything plus itself is just 2 times that anything. Now if this plus 320 is equal to 720,
- what plus 320 is 720? Well this thing must be equal to 400. Or, formally,
- subtract 320 from both sides of this. And you would get 400 is equal to 2w.
- So if 2 times something is equal to 400 that something must be 200.
- Or you can divide both sides of this equation by 2. Either way you will get the width is equal to 200 m.