Finding side lengths of rectangles given the perimeter
About this video
This video checks which side lengths could belong to a rectangle with a perimeter of 32 centimeters. It adds all four sides for each choice: 11 by 5 and 9 by 7 both give 32 cm, while 8 by 4 gives only 24 cm.
You'll be able to
- find the perimeter of a rectangle by adding all four sides.
- check whether a length and width give a certain perimeter.
- use number sense to rule out a choice before calculating.
Key words
- perimeter
- The total distance all the way around the outside of a shape.
- length and width
- The two different side measurements of a rectangle.
- rectangle
- A four-sided shape with square corners, where opposite sides are the same length.
Transcript
- [Educator] We are told, "A rectangle has a perimeter of 32 centimeters. Which of the following could be the length and width of the rectangle?" And they tell us to pick two answers. So pause this video, have a go at it before we do it together. Alright, well one way to do it is just to look at each of these choices and think about what that perimeter would be.
So let's say this one right over here, I'm gonna draw it small so we have space to do it. So let's say its height is 11 and its width is 5. And so if that's the case, then this other side, this other height on the other side of it, I guess you could say, is also 11.
And this top side is also 5. So what the perimeter going to be? This is going to be 11 + 5 + 11 + 5, which is equal to, let's see, 11 + 5 is 16, 11 + 5 is 16. 16 + 16 is 32 centimeters. So this one does have a perimeter of 32. So it could be the length and width of the rectangle.
So I like this one right here. Now let's look at this choice. Okay, and this one I can already, I have my spidey sense tells me that it's not going to add up because 8 is smaller than 11 and 4 is smaller than 5. So I don't think we're gonna get quite to 32 centimeters.
So, but let's just double check. So lemme draw another rectangle here. So this height is 8, 4. We have another 8, we have 4. Let's add them all together. We have 8 + 4 + 8 + 4, which is going to be 12 + 12. And my intuition was right, 12 + 12 is only 24 centimeters.
So we'll rule this one out. So this one is probably going to be the other choice 'cause it says pick two answers. But let's verify that. So we get a rectangle here. So this is 9 centimeters, this is 7 centimeters. This would be 9 as well. And then this would be 7.
So if we find the perimeter, it'd be 9 + 7 + 9 + 7. 9 + 7 + 9 + 7. 9 + 7 is equal to 16. 9 + 7 is 16. 16 + 16 is 32 centimeters. So yes, this one is also a correct answer.
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