How to Solve Proportions for Figures

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Solving proportions for figures always requires you to keep a few very important things in mind. Solve proportions for figures with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Number Theory Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to solve proportions for figures. Now, often times, these kinds of situations come up, whenever you're dealing with similar figures, whether it be similar triangles, similar rectangles, etc. And so, let's do an illustration as to how to set these up. Now, as I mentioned before, often times you're dealing with smaller and larger scales of figures. So, for example, if you're given that these triangles are similar to each other, you can make a few cases for the values, and that'll help you set up equations. So, let's just say, this was four and let's just say, this was 12 and let's just say, this was five and let's call it X. Then, it allows you set up proportional equations to allow you to solve them. Now, you have to make a decision though, do you want to put the smaller numbers on top, or do you want to put the larger numbers on top? Whatever decision you'll make, you just have to be consistent with it. So, let's just do smaller over larger. So, the idea here is, you have four over the corresponding side on the other triangle, four over 12, equals to, and that's going to be five over X. Now, regardless of which strategy you use, you still want to solve in a very consistent way. As you may have seen before, if you have fractions on either side of the equal sign, you use cross multiplication. So, the idea here is X times four, that's going to be four-X, and 12 times five is going to give you 60. So, solving for X here, divide both sides by four. So, you have X is equal to 15. So, if you had chosen to use the larger numbers on top, you would have got the same answers as well. But the bottom line here is, when it comes to proportions and figures, it often involves similar shapes. And that'll allow you to set up the equation, as long as you know what figures to plug in where. So, I'm Jimmy Chang and that's how to solve proportions in figures.

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