Altitudes...Helppppppppppppp?

Question

Why is the sum of 3 altitudes of a triangle always less than its perimeter?????

..I don't get it!!!!!!

Answer 1

You are not asking for a mathematical proof, so I'll presume that you just want to know why. In other words, you already know that the sum of 3 altitudes is always less than its perimeter, and it just doesn't make sense that this is the case.

Imagine a triangle. Any triangle. Okay. Now, imagine an altitude drawn from the top part (where the two sides meet) straight to the bottom.

I ask you this: How can you get that altitude to be higher?

The answer is you can't...UNLESS...you were to open up the top of the triangle, and make the sides have a smaller angle (say 40 degrees instead of 60 degrees). Of course, we are not doing this.

So, you are only measuring from the bottom of the triangle to the top, and that top part is at a height that is due to the side having some angle...except in the case of a right triangle, in which case, the other two sides will have an angle.

What I am saying is this: The side of a triangle is not at maximum height since it is angled. This means that all your measurements will be shorter than if they were standing straight up. Make sense??? If they were standing straight up, you'd just have three tall lines and not a triangle. So, since they are angled, your measurements are shorter than what they *could* be.

Yet with the perimeter, you always measure their FULL length.

So, as you noted, the sum of the altitudes will ALWAYS be less than the perimeter.

Regards,

Mysstere

Answer 2

answers.yahoo.com/question/index?qid=20061025222149AApVyYH
mathforum.org/library/drmath/sets/high_triangles.html?...
www.mathpropress.com/archive/iams/vol8.ascii
...www.mathpropress.com/archive/iams/vol8.ascii
answers.yahoo.com/my/profile?...&bestansfilter=1&link=answer
...answers.yahoo.com/question/index?qid=1006042924685