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

Identifying values in scale drawings


2m read
·Nov 11, 2024

We're told that figure A is a scale image of figure B. So that's figure A; this is figure B. Here, the scale that maps figure A to figure B is one to two and one half. What is the value of x?

All right, pause this video and see if you can figure it out. All right, so x is the length of this side right over here in figure A, and the corresponding side on figure B has length five.

One way to think about it is the ratio between x and five should be one to two and a half because that's the scale that goes from figure A to figure B. Figure A to figure B. So the ratio—let me write this out—the ratio between x and 5. So the ratio of x to 5, this should be an equivalent ratio as 1, one to two and a half.

And that one is hard to read; let me make a deeper blue. There you go! All right, so let's just think about how to do this. To go from two and a half to five, to go that way, you would multiply by two. So, to go from one to x, you would also multiply by two.

So the value of x is equal to two. If these are scaled up, you multiply this by two and a half, you get to five. So the scale factor is one to two and a half.

Let's do another example. We're told figure A is a scale image of figure B, and we see them both right over here. Once again, we need to figure out what x is going to be, and they don't give us the scale factor, but we can figure out the scale factor.

How do we do that? Well, we can see when you go from... of course, this side right over here corresponds to this side. It's the shorter side that forms a right angle with the base, and this is the longer side that forms a right angle with the base.

So you could set up some ratios. You could say look, the ratio of 3 to 4, you could say the ratio of 3 to 4. Let me do that blue color; the ratio of 3 to 4 is going to be the same thing as the ratio of x to 7.2. The ratio of x to 7.2, x to 7.2.

And so how do we figure out what x is going to be? Well, how do you go from 4 to 7.2? What do you have to multiply by? You might want to get out a calculator, or you might be able to do this in your head.

4 times 18 is 72, which is 2 times 36, which is 2 times 18. So 4 times 18 would be 72, or 4 times 1.8 would be 7.2. If you don't feel good about that mental arithmetic, you could just do the division.

4 goes into 7 one time. 1 times 4 is 4; subtract, you get a 3. You're gonna have your decimal right over there. Bring down the two. Thirty-two—4 goes into 32 eight times; 8 times 4 is 32, and we're done.

So to go from four to seven point two, you have to multiply by one point eight. And so to go from three to x, you also have to multiply by 1.8. And so x is 3 times 1.8.

What is that going to be? Well, 3 times 18 is... what? 30? It's 54. So this is going to be... let me verify that or show you that. 18 or 1.8 times 3.

3 times 8 is 24. 3 times 1 is 3 plus 2 is 5. One number behind the decimal point, 5.4, and we're done.

More Articles

View All
What language shows cause and effect? | Reading | Khan Academy
Hello readers! Once upon a time, in the previous century, there lived a cartoonist and engineer named Rube Goldberg, who became well known for his drawings of wacky, over-complicated machines. This is one such machine: the self-operating napkin. You see h…
Analyzing graphs of exponential functions | High School Math | Khan Academy
So we have the graph of an exponential function here, and the function is m of x. What I want to do is figure out what m of 6 is going to be equal to. And like always, pause the video and see if you can work it out. Well, as I mentioned, this is an expon…
Light dependent reactions actors
In a previous video, we gave an overview of the light-dependent reactions, which are essentially occurring across the thylakoid membranes. Right, and we zoomed in on one, and we saw, okay, we have some energy from light exciting the electrons within the c…
Marginal revenue and marginal cost in imperfect competition | APⓇ Microeconomics | Khan Academy
In this video, we’re going to think about marginal revenue and marginal cost for a firm in an imperfectly competitive market. But before we do that, I just want to be able to review and compare to what we already know about a firm in a perfectly competiti…
How to catch a Dwarf Planet -- Triton MM#3
The 14 moons of Neptune are a strange bunch. Most of them are small, potato-shaped pieces of ice and rock. Some are so far away from Neptune that they need 29 years to circle Neptune once. Almost all of them are asteroids trapped by Neptune’s gravity. 99…
Homeroom with Sal & Pedro Noguera - Wednesday, October 21
Hi everyone, Sal Khan here. Welcome to the Homeroom live stream. We have a really exciting guest today, Pedro Noguera, who is the Dean of the Rossier School of Education at the University of Southern California. So start thinking of your questions, puttin…