yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Scaling perimeter and area example 2 | Transformational geometry | Grade 8 (TX) | Khan Academy


2m read
·Nov 10, 2024

We're told quadrilateral A was dilated by a scale factor of 2/3 to create quadrilateral B. Complete the missing measurements in the table below. So like always, pause this video and then we will do this together. Try to do it yourself, and then we'll do it together.

All right, so in previous videos, we talked about if you have a scale factor, perimeter is going to be scaled by the same amount, while area is going to be scaled by the square of that. So perimeter is also going to be scaled by 2/3. So 30 * 2/3… let me write that a little bit neater. So times 2/3 is going to be 20.

Then the 54 is going to be scaled by (2/3) squared. One way to think about it is, you're scaling in each dimension by 2/3, and so when you multiply the two dimensions to get area, you're going to be multiplying by 2/3 twice to get the new scaled area. So what is (2/3) squared? Well, that is the same thing as 4/9. So what is 54 * (4/9)?

That is equal to 54 * (4 over 9). Both 54 and 9 are divisible by 9, so let's divide them both by 9. This becomes 6, and this becomes 1. So we end up with 6 * 4, which is equal to 24, and we're done.

Now to make this very tangible in your head, let's give an example of where this could actually happen. Let's imagine that quadrilateral A, let's say it looked like this, and I think I can eyeball it. Let's say that that dimension is 6, and that dimension is 9. I think that adds up: 6 plus 6 is 12, and 9 plus 9 is 18. So yes, this perimeter is 30, and the area here is actually 54.

So this is actually the example of quadrilateral A over here. And now quadrilateral B, if we're scaling it by 2/3, then all of these dimensions are going to be scaled by 2/3. So quadrilateral B will, instead of having a length of—or height of—6 over here, it's going to have a height of 4, and instead of having a length or width of 9 here, it's going to be 2/3 of that. It's going to be 6.

So the quadrilateral will look like this, and we can verify that the perimeter now is going to be 4 plus 4, which is 8, plus 6, plus 6, which is 12. So it's 8 plus 12, which is 20, and the new area is 6 * 4, which is 24. Now, you didn't have to do this, but I just wanted to make sure you understood why this was happening.

More Articles

View All
Khanmigo for Districts
[Music] Introducing Con Migo for districts. Khan Academy’s AI-powered student tutor and teaching assistant is paving the way for a new era of learning in the classroom. I could see it as a teacher virtual assistant. I could see it as a virtual assistant …
How To Embody A MILLIONAIRE'S Lifestyle | Kevin O'Leary
I keep telling everybody every time we talk about investing, the key is diversification. I feel good about the expense, but I also feel good from an investment strategy that it’s not just frivolous and stupid; that I needed to get my money back out of it.…
This 18th Century Gold Rush Changed How the World Pans for Gold | National Geographic
Gold is the most powerful metal on earth, and Russia is one of the world’s leading suppliers of it. It all began in 1745 when a peasant named Tiara Fade Markov, while looking for crystal, found something else: a tiny gold speck inside a piece of quartz. H…
Mind Reading
Mind reading? Of course not. I love reading. Look, mind reading might sound like pseudoscientific—pardon my language—bullshoot. But its scientific counterpart, thought identification, is very much a real thing. It’s based in neuroimaging and machine learn…
A Steam Pit Celebration | Live Free or Die
[Music] Yeah, that’s good. Even these rim rocks are pretty warm, but most importantly, everything below the ground level’s red hot under there. Matt’s putting the finishing touches on the primitive pit he’ll use to roast his wild turkey, but it’s a delic…
Ray Dalio on The Big Debt Cycle
Just frame for us your thoughts on debt for a second. How do you think about debt as an absolute construct or a relative construct, especially sovereign debt? You know, there is a US debt, but then there are also every other 182 countries who have a ton o…