anonymous
  • anonymous
Two sides of a triangle have lengths of 5x and 11x. The length of the third ide can be any number between ___ and ___.
Mathematics
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anonymous
  • anonymous
Two sides of a triangle have lengths of 5x and 11x. The length of the third ide can be any number between ___ and ___.
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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nowhereman
  • nowhereman
You have to apply the triangle inequality!
anonymous
  • anonymous
I don't know how, though. I'm trying to understand it, can you walk me through it?
nowhereman
  • nowhereman
It's a basic property of a triange: The sum of two side length must always be bigger then the third side length. It comes from the fact, that the sides of a triangle are the shortest connections between the points and if you take the connection going over the third point, you must get a longer path. So if the side length are called a, b and c you get \[\begin{gather}a+b \geq c\\b+c \geq a\\c+a \geq b\end{gather}\]

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nowhereman
  • nowhereman
Now just insert the given length and see which inequality gives you a range for the third side.

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