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## 7th grade

### Unit 4: Lesson 4

Identifying proportional relationships- Intro to proportional relationships
- Proportional relationships: movie tickets
- Proportional relationships: bananas
- Proportional relationships: spaghetti
- Identify proportional relationships
- Proportional relationships
- Proportional relationships
- Is side length & area proportional?
- Is side length & perimeter proportional?

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# Is side length & perimeter proportional?

Sal answers the question by drawing a square and thinking about the relationship between side length and perimeter.

## Want to join the conversation?

- Are the length and breadth of different rectangles of the same perimeter in proportion. Examine.(7 votes)
- what does proportional mean??(4 votes)
- or this (of two quantities) having the same or a constant ratio or relation:

The quantities y and x are proportional if y/x = k, where k is the constant of proportionality.(6 votes)

- I understand this for a sqaure, but what If it's for a rectangle how would te sides be porportional since a rectangles has not all 4 sides that are congurent.(3 votes)
- If this is for a rectangle, the ratio won't be proportional any more. For rectangles can have any number from 1 to infinity for two of the sides and another number from 1 to infinity for the other two sides. If the 4 sides are the same, you get a special rectangle that you call a square.

For example, two sides of the rectangle are 4 and the other two are 6. Then the perimeter would be 4+4+6+6 which is 20, then do 20 divided one of the sides to get the proportion, for example, 20 divided 4, then you will get 5. Then get another rectangle, let's say two sides are 7 and the other two are 9. then you would have 32 for the perimeter, then 32 divided 8, and you get 4.

And now we have a proportion of 5 and another of 4. This is not a proportional relationship.

Hopefully this helps.(2 votes)

- What happens when you only have x on one side?(0 votes)
- well it can depend on what the other sides are since you said that one side of the square is x then all of the other sides are x as well ( all sides of a square are equal)(1 vote)

- Is this directly proportional or inversely proportional? Especially if we're looking for the perimeter of a rectangle.(2 votes)
- Nice cool doing this with us(2 votes)
- why do you repeat when you say "side length" because then i hear "siiiiiide length, side length"(2 votes)
- How can ratio's help us in REAL LIFE.(2 votes)
- It can help for calculating things, such as calculating the amount of plastic in a ocean. Say, for everyone 4 pounds of plastic there’s 1 pound of cardboard! That can help determine how much trash there is!(1 vote)

- Thanks a bunch! This made the unit so much easier!(2 votes)
- i love your video(2 votes)

## 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.