Is it possible to construct an equilateral triangle with the altitude having the same measure as one of the sides?
2007-01-06 23:54:38 · 11 answers · asked by amitpop22 2 in Science & Mathematics ➔ Mathematics
No. The altitude of an equilateral triangle divides the triangle into two 30-60-90 triangles. The lon leg of a 30-60-90 triangle is sqrt(3) times as long as the shorter leg.. Thus you would have to show that sqrt(3)*x=2x in order to have an altitude that is equal to a side. And, since sqrt(3) is not equal to 2, it is not possible.
2007-01-06 23:59:14 · answer #1 · answered by dwobbit 2 · 0⤊ 0⤋
Well, draw an equilateral triangle. The altitude is not the same measure. Why don't you try to draw an equilateral triangle using a ruler? Then measure the altitude and place it on all three lines that form the 3 sides.
Guido
2007-01-06 23:59:19 · answer #2 · answered by Anonymous · 0⤊ 0⤋
When you draw the altitude, you make 2 right triangles. The sides from the original equilateral triangle become the hypotenuse, and we all know that the hypotenuse is the longest side of a triangle.
2007-01-07 01:54:53 · answer #3 · answered by Brian S 2 · 0⤊ 0⤋
It depends on what type of equilateral triangle,
and on what type of surface it is drawn.
It's not possible on a 2-dimensional plane,
but it is possible on a sphere.
2007-01-07 00:21:55 · answer #4 · answered by falzoon 7 · 0⤊ 0⤋
No way. This is not possible as it will violate all definitions of eq triangle and altitudes.
2007-01-07 01:05:19 · answer #5 · answered by nayanmange 4 · 0⤊ 0⤋
no, you cannot even construct an isosceles nor scalene triangle with that. a triangle's because a triangle's altitude is always shorter than its leg.. it cannot possibly be equal nor longer.
2007-01-07 00:26:00 · answer #6 · answered by dee 1 · 0⤊ 0⤋
Impossible.
2007-01-07 00:06:55 · answer #7 · answered by Nightstalker1967 4 · 0⤊ 0⤋
all 3 sides must be the same.
2007-01-06 23:56:22 · answer #8 · answered by silentjealousy77 4 · 0⤊ 0⤋
Not a chance!
2007-01-06 23:56:50 · answer #9 · answered by yahoo 6 · 0⤊ 0⤋
no by definition
2007-01-07 00:18:25 · answer #10 · answered by mathman241 6 · 0⤊ 0⤋