# How to Solve Problems Involving Similar Figures

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Solving problems involving similar figures is something you might do if you had two triangles, for example. Solve problems involving similar figures with help from an experienced mathematics educator in this free video clip.

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## Video Transcript

Hi, my name is Marija, and today I'm going to show you how to solve problems involving similar figures. So if I give you two triangles, one smaller, one larger, that you're told are similar, I would have to give you the dimensions or at least two of the dimensions of one of them. So I'm going to say that this side is two inches, this one is three inches, this one is four and this one we don't know and we're trying to find. So if you're told that the two figures are similar, that means that their sides are proportionate. So the rate at which the two to the four is the same as the rate at which the three will go in to this larger side. So what we'll do to solve this is set up a proportion using the values we have. So I'll set up a ratio with the smaller triangle of two over three. And then I'll set up another ratio with a larger one, making sure that the side that corresponds to the two is in the numerator just like the two is. So the side that corresponds to the two is the four. So that four is going to go in the numerator. And then because I don't know what the x value is, that's going to go in the denominator with its corresponding side three. And now to solve the proportion, we just cross multiply, two times x is two x, bring down your equal sign, three times four is 12, now we're going to divide by two on both sides to solve the equation and when we do that we get x equals six meaning that this side of the triangle is six. So you can see that this first side of two grew in to a four by doubling and then the three grew in to a six, also by doubling. Showing that it's a proportional relationship.

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