Identifying values in scale copies

- [Instructor] 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 1/2. 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 on Figure A, and the corresponding side on Figure B has length five. And so, 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 five, so the ratio of X to five, this should be an equivalent ratio as one, one to two and a half. One to two and a half, and that one is hard to read, let me make it a deeper blue, there you go. All right, so let's just think about how to do this. To go from from two and a half to five, to go that way, you would multiply be two, so to go from one to X, you would also multiple by two. So, the value of X is equal to two. If these are scaled up, you multiple 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, and once again, we gotta 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, this side right over here corresponds to this side. It's the shorter side that forms a right angle with the base, this is the longer side that forms a right angle with the base, and so, you could set up some ratios. You can say, look, the ratio of three to four, you can say the ratio of three to four, we need that blue color, the ratio of three to four 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 four to 7.2? What do you have to multiply by? You might wanna get out a calculator or you might be able to do this in your head. Four 72 is two times 36, which is two times 18, so four times 18 would be 72 or four times 1.8 would be 7.2, and if you don't feel good about that mental arithmetic, you could just do the division. Four goes into seven one time, one times four is four, subtract, you get a three, you're gonna have your decimal right over there, bring down the two, 32, four goes into 32 eight times, eight times four is 32, and we're done. So, to go from four to 7.2, you have to multiply by 1.8 and so, to go from three to X, you also have to multiply by 1.8. And so, X is three times 1.8, what is that going to be? Well, three times 18 is, what? 30, it's 54, so this is going to be 5.4. Let me verify that or show you that. 18 or 1.8 times three, three times eight is 24, three times one is three, plus two is five, one number behind the decimal point, 5.4 and we're done.