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公制系統的應用 (英) : 公制系統的應用
- The perimeter of a rectangular fence measures 0.72
- 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
- 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.