What is the perimeter of an equilateral triangle whose height is 2radical3?
2006-10-02 11:21:36 · 6 answers · asked by princesschristine91 1 in Science & Mathematics ➔ Mathematics
how do you do this problem?
2006-10-02 11:30:26 · update #1
Divide your equilateral triangle into a pair of 30-60-90 right triangles.
The ratio of the sides of a 30-60-90 triangle are 1, 2, √3, which you can confirm with the pythagorean theorem. In your case, you have double this or 2, 4, 2√3.
Done algebraically, take the side to be S units. That would be the hypotenuse of your 30-60-90 triangle. And one leg would be S/2 (half the length) and the other is 2√3 (height).
S² = (S/2)² + (2√3)²
S² = S²/4 + 2² * (√3)²
S² - S²/4 = 4 * 3
3/4 S² = 12
S² = 4/3 (12)
S² = 16
S = 4 (it can't be -4 because it is a length)
So each side of the triangle is 4 units (half the side is 2 units and the height is 2√3 units).
The perimeter is simply 3 x 4 = 12.
Therefore the perimeter is 12 units.
2006-10-02 11:31:01 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
12
2006-10-02 18:30:53 · answer #2 · answered by Alex Alonso 1 · 0⤊ 0⤋
12
2006-10-02 18:29:48 · answer #3 · answered by greendayrox 2 · 0⤊ 0⤋
12
2006-10-02 18:25:33 · answer #4 · answered by Greg G 5 · 0⤊ 0⤋
12 units
2006-10-02 18:24:43 · answer #5 · answered by Anonymous · 0⤊ 1⤋
if 2radical3 means twice the square-root of 3 then I'm with Greg.
2006-10-02 18:34:25 · answer #6 · answered by Anonymous · 0⤊ 0⤋