If the altitude of a triangle has length 6 root, what is the perimeter of the triangle?
2007-01-17 13:14:37 · 3 answers · asked by Kate! 3 in Science & Mathematics ➔ Mathematics
It is equilateral
2007-01-17 13:36:56 · update #1
for that, you have to also give either the angles in the triangle or the length of the base.... cool, it's equilateral? okay then.
draw a diagram first of all, that helps. if you drop an altitude down the equilateral triangle (which means all three angles are 60 degrees), you will bisect one of the angles and will be left with 2 30-60-90 triangle. the properties of that are the short side (the bottom of the triangle) equals 1/2 of the hypotenuse and the short side is (sqrt3)-times the length of the longest leg (the altitude). so, (and I'm sure this makes more sense if you draw it) make the bottom of one of the 30-60-90 triangles x, and the altitude length 6 = x*(sqrt3) which means x = 6(sqrt3)/3, or 2sqrt3 for the short side. Now, multiply it by two so you can have the full length of the original side for the equilateral triangle, and it's 4sqrt3. perimeter is 3s, so the perimeter = 12sqrt3
I'm sure I could've explained it better. but yeah, that's how you do it.
2007-01-17 13:17:51 · answer #1 · answered by car of boat 4 · 0⤊ 0⤋
The question is incomplete Is it an equilateral triangle?Then the perimeter can be found out from the altitude.
2007-01-17 21:28:53 · answer #2 · answered by alpha 7 · 0⤊ 0⤋
The altitude is one thing. The base can still be anything from 0.0000001 to 1000000000 (you get the point). The perimeter will be dependent on this.
If you know that it is an equilateral triangle, then that's another story.
2007-01-17 21:19:53 · answer #3 · answered by Dave 6 · 0⤊ 0⤋