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Sides of triangles ratio and angles

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by sparkles3144 » Thu Apr 25, 2013 1:02 pm
The ratios between sides of the triangle are
3:4:5 or 5:12:13

Is it possible for them to be some other triangle other than right triangle?

I am not sure if my question makes sense.

Please let me know if it does not make sense.

Thank you so much!
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by Ben.Miller@ApexGMAT » Thu Apr 25, 2013 2:44 pm
Your question makes perfect sense.

The short answer is NO. 3:4:5 and 5:12:13 triangles are always right triangles.

Here's why:

Any 3 sides can only be put together in one configuration to make a closed shape. This configuration produces a set of unique angles as well.

Reversing this, a set of 3 angles will always have the same sides.

This is the basis of trigonometry. While you can make the triangle bigger or smaller, the ratios between the sides ALWAYS stay the same.

Ben
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