Perimeter word problem (tables) | Math | 3rd grade | Khan Academy

Leah and Pedro push two tables together. The figure below shows the new arrangement. So we have table number one and table number two that Leah and Pedro have pushed together. Maybe they're having a bunch of people over for a fancy breakfast. They've pushed two tables together to have a lot of room for people to sit.

We 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. So what we could do is say here we know there's 3 m around the outside. Here's another meter, so that's 4 m around the outside. But then we get to here, and uh-oh, we don't have this one, and we don't have this side length or this length or 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 because these tables are rectangles. Opposite sides are equal, so if this side down here is 1 m, then this side up here has to be 1 m. Same here: if this is 3 m, the opposite side is also 3 m. We have 1 meter on the end of this table, so the inside, this length from here to here, is also 1 m. But 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's why.

This length and this length are part of the outside, and we need to know how long those are. So what we can say is if this entire length is 3 m, then this entire length is 3 m, but one of those meters was moved to the inside. So how many meters are still left here on the outside? We had 3 m over here; we moved one to the inside, so we have 2 m left on the outside. So this length and this length are a total of 2 m. We can't know for sure; they look pretty evenly divided. We can't know for sure that they're both 1 meter, but we do know for sure that it's a total of 2 m when we can add them.

So 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. Okay, now everything is labeled, so we can get back to finding the perimeter. The distance around the outside will be all of these lengths put together. So here we have 1 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 long side of three, and finally one more meter going up the side.

So we can add these lengths. When we combine these links, they'll tell us the total distance around the outside: 1 + 3 is 4 + 1 more is 5 + 1 more is 6; 6 + 3 is 9; 9 + 1 is 10; 10 + 3 is 13; and 13 + 1 more is 14. So the perimeter of the new figure, of this new table arrangement, is 14 m.