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How to find the length of two sides of a triangle, whose ratio is 3:5? Please read description.

I have triangle ABC. The longest length is AB=12. AC and BC have a ratio of 3:5. I don't know how to find out what AC and BC equal. How do I find the lengths?

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I tried

Not sure

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Thank you so much!! It worked!
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What kind of triangle

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There are too many answers, one answer could be 6 and 10 and an other could be 9 and 15 but don't ask me how?

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andranik, I was considering this problem as a "right triangle" problem, and in order for it to work, the ratios of the three sides would be 3, 5, and a 5.83095.

The 5.83095 would be the side that is 12(whatever measurement) long. That being the case there is only one answer for the two unknown sides.

Your answer of (6, and 10), or (9, and 15) is wrong.
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Okay now that I have more time let me explain. The question involved must be for a right angle triangle, as there is not enough information to solve for any other kind of triangle. Being as we must assume that it is a right angle triangle, then the solution presents itself through the simple calculations I used in the post.

Your answer confuses the ratio 3:5 as being a certain length, such as a 6 on one side and a 10 on the other side. But a length of 6 on one side and 10 on the other will not give you a 12 on a right triangles longest side.
6x6 (36) and a 10x10 (100) equals 136 which is well below the 12x12 (144) needed to equal the longest side. - so this answer is wrong.

The 9, and 15 is wrong without having to calculate because as previously stated, the longest side is 12, and a 15 breaks this rule.

So only one answer can be given for a right angle triangle who's longest side is 12 and the ratio to the other two sides is a 3:5 ratio.

If the question was for a triangle that wasn't a right angle, then you would have to have more information in order to solve for it.
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If AB = 12, and it is the longest side, then the other two sides follow this formula.

The square of side AC + the square of side BC = the square of AB

The square of AB is (12x12) = 144 so the sum of the square of the other two sides must equal 144

Now we don't know yet the lengths of the other two sides but only their ratios to each other

If one of the other sides is 3 units in length, and the other side is 5 units in length, then you can say that 3 squared, plus 5 squared must equal the square of the length of AB, which is 12 squared, or 144.

The ratios of 3 squared = 9 and 5 squared = 25 and the sum of both squares add up to the sum of 34

The square root of 34 is 5.83095

And this ratio of 5.83095 must give us our length of 12.

12 divided by 5.83095 = 2.057984 which equals a unit of 1

3 units x 2.057984 = 6.173

5 units x 2.057984 = 10.29

According to the formula, the 6.173 squared, plus the 10.29 squared, needs to equal the side that we know is 12 long, squared, or 144. Lets verify this.

6.173 squared is 38.106 and 10.2899 squared is 105.884 and the squares add up to
143.99 which is real close to 144.

So one side of your triangle is 6.173 in length, the other side is 10.29 and your longest side, which you already had is 12 in length.

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Hi dear dusty_matter
The formula you used ( the Sum square of tow shorter sides is equal to square of longest side ) it works only in right triangle, the answer you found is only one of the infinity answers.
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andranik, I was considering this problem as a "right triangle" problem, and in order for it to work, the ratios of the three sides would be 3, 5, and a 5.83095.

The 5.83095 would be the side that is 12(whatever measurement) long. That being the case there is only one answer.
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Dusty-matter, where in the question is asked for right triangle? Let's say it is a right triangle, then you should check your answer by the same formula as you checked mine which you will see you answer is wrong for even a right angle triangle too.
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