Prove that a height of a triangle is smaller than side

[Guest]

Prove that a height of a triangle is smaller than at least one side.

[leesajohnson]

Please provide all the data for the question.

[Guest]

The question..... Prove that a height of a triangle is smaller than at least one side.

You ask.......
Please provide all the data for the question.

The details.........
The question means exactly as it says.......
The height of a triangle is smaller than at least one side......because.......
The height of a triangle is always smaller than its longest side
If right angled then the height is equal to its vertical side and smaller than the sloping side.

[Guest]

If you are trying to say that in any triangle there exist at least one altitude that is longer than at least one side, that is wrong! Take, for example, an equilateral triangle with all sides of length 2. Then it is easy to show that every altitude has length [tex]\sqrt{3}[/tex] which is less than two.