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# Applying the metric system to perimeter

## Video transcript

the perimeter of a rectangular fence measure 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 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 0.2 kilometers that's the total distance of all of the sides now the length of the fenced area is 160 meters so let's call this the length so this distance right here 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 the this length Plus this length Plus that length Plus that length so it's going to be so the perimeter let me write it in orange the perimeter perimeter is going to be equal to W the width plus 160 meters plus 160 meters plus the width plus the width plus 160 meters plus 160 meters plus 160 meters and let's assume W is in meters so it's W that 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 so if you were to add all of these up you have a W plus 2w so you would be 2 W 2 W plus 160 plus 160 is 320 so that's 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 per defense is 0.72 kilometers so the perimeter let me do that same orange color the perimeter perimeter is also equal to 0.72 kilometers and we can abbreviate that with K M now if we wanted to solve an equation if we wanted to set this thing equal to the total number the 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 what's 1,000 meters for every one kilometer one 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 a thousand you could just first say okay let's take 72 times a thousand 72 times a thousand would be 72 with three zeros 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 a thousand is 720 and that makes sense 0.72 it's not quite a it's not quite one but it's getting close to one almost 3/4 of a whole and this is almost 3/4 of a thousand 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 so if you take 2 times the width in meters and add that to the length and the combined lengths it's 160 160 that's 320 and all of this is in meters all of this is in meters that is going to be equal to the total perimeter which is 720 meters is equal to 720 meters now that we have the unit's right we can solve for W and W will tell us this within meters and meters so to W plus 320 is equal to 720 we can subtract 3 20 from both sides of this equation remember an equation saying that is equal to that if we want them both always to be equal whatever we do the left-hand side we have to do the right-hand side so we subtract 3 20 from both sides subtract 3 20 from both sides the left hand side that cancels out that's why we subtracted 320 and you're just you just have left 2 times the width is equal to 720 minus 320 is 400 now you can divide both sides of this by 2 divide both sides by 2 and then you're left with W is equal to 400 over 2 which is 200 which is 200 and we said that W was in meters so the width is 200 the width is 200 meters so this is 200 meters this is 200 meters and 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