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周長與單位轉換 (英)

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周長與單位轉換 (英) : 周長與單位轉換

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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.

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周長與單位轉換 (英)

周長與單位轉換 (英) : 周長與單位轉換