Grade 6 (Virginia)
Perimeter word problem: tables
Lindsay solves a perimeter word problem that involves combining two perimeters. Created by Lindsay Spears.
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- [Voiceover] Lea and Pedro push two tables together. The figure below shows the new arrangement. We have table number one and table number two that Lea and Pedro have pushed together. Maybe they're having a bunch of people over for a fancy breakfast and so they've pushed one, two tables together to have a lot of room for people to sit. We're asked, what is the perimeter of the new figure? Perimeter is the distance around the outside, so all of this space around the outside is the perimeter and we need to figure that out. What we could do we could say, "Here we know there is three meters around the outside, here is another meter, so that's four meters around the outside." Then we get to here and oh, oh we don't have this one and we don't have this side length, through this length, through this length, so we can't know the entire distance around the outside until we figure out what those missing side lengths are. Let's fill in some of those first. These tables are rectangles, opposite sides are equal. If this side down here is one meter, then the side up here has to be one meter. Same here if this is three meters, the opposite side is also three meters. We have one meter on the end of this table so that inside this length from here to here is also one meter. That's an interesting one, this one meter here because this part now right here, that's on the inside of the arrangement. That's not the outside, so that is not part of the perimeter. This one meter will not be included in our perimeter but it is still important to us and here is why. This length and this length are part of the outside and we need to know how long those are. What we can say is, if this entire length is three meters, then this entire length is three meters, but one of those meters was moved to the inside, so how many meters are still left here on the outside? We had three meters over here, we moved one to the inside, so we have two meters left on the outside. This length and this length are a total of two meters. We can't know for sure, they look pretty evenly divided, we can't know for sure that they're both one meter but we do know for sure that it's a total of two meters when we combine them. Again this one meter is not on the outside, it's not part of our perimeter but it did help us to find the other lengths. Now everything is labelled, so we can get back to finding the perimeter, the distance around the outside will be all of these lengths put together. Here we have one meter plus moving down the outside three more meters, plus one more, plus one here on that side we just figured out, plus another three, one on the end, another alongside of three and finally one more meter going up the side. We can add these lengths. When we combine these lengths they'll tell us the total distance around the outside. One plus three is four, plus one more is five, plus one more is six, six plus three is nine, nine plus one is 10, 10 plus three is 13 and 13 plus one more is 14. The perimeter of the new figure, of this new table arrangement is 14 meters.