Using multiplication to compare perimeters of rectangles
About this video
Mark's rectangle is 6 cm by 4 cm. Olga's rectangle has sides 3 times as long, so it is 18 cm by 12 cm with a perimeter of 60 cm. The video then shows that Mark's perimeter is 20 cm, so when every side is 3 times as long, the perimeter is also 3 times as long.
You'll be able to
- find side lengths that are a number of times as long as other side lengths.
- find the perimeter of a rectangle by adding all four sides.
- explain why multiplying every side by 3 multiplies the perimeter by 3.
Key words
- perimeter
- The total distance around a shape, like a fence around a field.
- three times as long
- A length you get by multiplying another length by 3.
- corresponding sides
- Sides that match up in the same position on two similar shapes.
Transcript
- [Instructor] We're told that Mark draws a rectangle that is six centimeters by four centimeters. We can see that here. Olga draws a rectangle with side lengths that are three times as long as Mark's rectangle. What is the perimeter of Olga's rectangle. Pause this video and see if you can figure that out.
All right, now let's do this together. So I'm not gonna quite draw it to scale, but let me draw another rectangle here. That would be Olga's rectangle. In fact, I definitely don't have space to draw it at scale, but it might look something like this, where the corresponding sides, or if we look at the height right here, instead of four centimeters, we're gonna be three times as long as that.
So if we multiply that times three, we're going to 12 centimeters and instead of six centimeters, if we multiply that times three, we'd get to 18 centimeters. So Olga's rectangle is going to be 12 centimeters by 18 centimeters. So what's the perimeter of Olga's rectangle going to be?
Well, it's going to be the sum of all of these sides right over here. So it's gonna be 12 centimeters plus this 18 centimeters, plus this 12 centimeters. We're going all the way around, it's like building a fence around a piece of property. So plus another 12 and then plus another 18 centimeters.
We have four sides, so we should list all of their lengths over here. So what is this going to be? This is 12 plus 18 is 30. We have another 30 right here, 12 plus 18. So this is 30 plus 30, which is equal to 60 centimeters and we're officially done. Now one interesting thing is to compare that perimeter to Mark's rectangle.
So what's the perimeter for Mark's rectangle? Well, that height on the other side is also going to be four centimeters. This appears going to be six centimeters. So this is going to be four plus six, plus four plus six, which is 10 plus 10, which is equal to 20 centimeters.
Now notice Olga's rectangle, each side is three times as long. And the perimeter, the sum of all the sides combined is also three times as long. And that makes sense. If you did three times each of every one of these, it makes sense that it would make this sum of them the perimeter three times longer.
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