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Solving Proportions - Concept
Solving proportions is a crucial skill when studying similar polygons. The ratio of corresponding side lengths between similar polygons are equal and two equivalent ratios are a proportion. For solving proportions problems, we set up the proportions and solve for the missing side length - it will be a variable, or a variable expression.
When you're talking about similarity, 2 figures that are similar, you're going to be using proportions. So just because we've moved on beyond Algebra doesn't mean that you can forget it.
A ratio is just one relationship between two different numbers. A proportion is when you say that two ratios are equal to each other. And you'll be using these all throughout your similarity unit.
So let's look at one quick example here. If I gave you this proportion, and I asked you to solve it for x, the way that you were taught back in grade school still applies. You could cross multiply. So we could say that x times 21, is equal to 7 times 18. So Math teachers cringe a little bit when they just say cross multiply but it will work for Geometry.
So to solve this for x, we're going to divide both sides by 21. Now notice that I didn't multiply 7 times 18. I'm going to use factors to simplify here. So I'm going to write 21 as the product of 7 times 3. Now I can cancel out the sevens and see that I have 18 divided by 3. Which means x must be 6.
There's multiple ways to solve proportions. But this way that you're shown will always work. Where you cross multiply and then you have to divide by whatever numbers multiplying your variable.