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# Is side length & perimeter proportional?

## Video transcript

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 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 make three columns and on the first column we're going to think about the side lengths side length and that's measured as X and in the next column I want to think about the perimeter perimeter well what is that that's going to be X plus X plus X plus X which is of course 4x and then I want to think about the ratio the ratio between perimeter me between perimeter perimeter and a side length 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 is going to be four times two it's going to be eight so the ratio is 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 side lengths it looks like it's always going to be four and we could do keep going here if our side length is 3 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 you're the ratio of perimeter to side length it's always going to be it's always going to be the perimeter is going to be 4x if the side length is X and 4x divided by X well that's always going to be 4 well this definitely meets our conditions for being a proportional relationship the ratio between perimeter and side lengths is always going to be 4 we didn't have to do this table here but this makes it a little bit more concrete it's or we could write it like this we could write that perimeter perimeter perimeter for a square is equal to four times the side length side 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