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# Is side length & perimeter proportional?

CCSS Math: 7.RP.A.2b

## Video transcript

- [Voiceover] We have a square here and all the sides have length x. And what I want to think about here is whether the perimeter of the square is proportional to the length of a side of the square. So let's think about it a little bit. I'm going to draw a table, so let me make some columns here. So there you have that, we have that, and we'll make three columns and on the first column we're going to think about the Side length. Side length, and that's measured as x. And in the next column I want to think about the Perimeter. Well what is that? That's going to be x plus x plus x plus x which is, of course, four x. And then I want to think about the ratio. The ratio between Perimeter, Perimeter and Side length. So let's see, when the Side length is equal to one, what's the Perimeter? It's going to be four times one. One plus one plus one plus one. It's going to be four. And what's our ratio? It's going to be four to one which, of course, is equal to four. Now what if the Side length is two? Well then the Perimeter is going to be two plus two plus two plus two. It's going to be four times two. That's going to be eight. So the ratio's going to be eight to two which is going to be equal to four. I think we see a pattern here. The ratio of Perimeter to Side length, it looks like it's always going to be four. Now we could keep going here. If our Side length is three, then our Perimeter is going to be 12. What's the ratio? 12 divided by three is equal to four. Now this isn't some magical thing here, because to figure out the Perimeter we're multiplying it by four. So if the ratio of Perimeter to Side length, it's always going to be, the Perimeter is going to be four x if the Side length is x, and four x divided by x, well that's always going to be four. Well this definitely meets our conditions for being a proportional relationship. The ratio between Perimeter and Side length is always going to be four. We didn't have to do this table here, but this makes it a little bit more concrete. Or we could write it like this, we could write that Perimeter for a square is equal to four times the Side length. And so, once again, it becomes clear it's a proportional relationship. The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.