SOLUTION: 18. One triangle has sides measuring 3�, 6�, and 9�. A similar triangle has sides measuring 5� and 15�. Find the length of the missing side. I need help thanks so very much!

Question 635832: 18. One triangle has sides measuring 3�, 6�, and 9�. A similar triangle has sides measuring 5� and 15�. Find the length of the missing side.
I need help thanks so very much!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The sides of similar triangles are proportional. This means that if you make a ratio out of any two corresponding sides, then it works out the same as when you make a ratio out of another pair of corresponding sides.

So to solve your problem we need to figure out which sides correspond to each other. We can do this by trial and error. Let's start by making a ratio out of two sides:

Now can we form another ratio use a different pair of sides that works out the same? Answer: Yes. We can use
which reduces to

And try as you might, there are no other combinations that result in equal ratios. Since the 3 and 5 inch side correspond and the 9 and 15 inch sides correspond, the 6" side must correspond to the missing side.

We already know what the ratio of that third pair of sides will work out to be, 3/5. We can use this to find the third side:

Solving this for x we should find that x = 10. So the missing side is 10".
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