The altitude of an equilateral triangle is 6 square 3 units long. The length of one side of the triangle is ____ units.

You must mean 6 square root of 3, or 6√3

let each side be 2x
then
x^2 + (6√3)^2 = (2x)^2
x^2 + 108 = 4x^2
3x^2 = 108
x^2 = 36
x = 6

So each side is 12 units long

Well, if the altitude of an equilateral triangle is 6√3 units long, then you can be certain that it's not a triangle made by acrophobic clowns! As for the length of one side, let's think about it. Since an equilateral triangle has equal sides, we can divide it into two right-angled triangles. The altitude we're given is the hypotenuse of one of these right triangles. Now if we know the altitude and we remember some basic trigonometry, we can use the sine function to find the length of one side. So, since sin(60 degrees) = opposite/hypotenuse, we can say sin(60 degrees) = x/6√3. Solving for x, we get x = 6 units. Ta-da! The length of one side of the triangle is 6 units. Remember, no need to clown around with math, it's all about using our mathematical tricks!

To find the length of one side of an equilateral triangle, we can use the formula:

Side length = (2 * Altitude) / √3

Given that the altitude of the equilateral triangle is 6√3 units long, we can substitute this value into the formula:

Side length = (2 * 6√3) / √3
Side length = (12√3) / √3

Since the square root of 3 divided by itself equals 1, we can simplify the expression:

Side length = 12 units

Therefore, the length of one side of the equilateral triangle is 12 units.

To find the length of one side of the equilateral triangle, we can use the formula for the area of an equilateral triangle.

The area of an equilateral triangle is given by the formula: Area = (s^2 * √3) / 4, where s is the length of one side.

Given that the altitude of the equilateral triangle is 6√3 units, we know that the altitude is equal to the height of the triangle, and the height bisects the base, forming a right angle.

We can use the Pythagorean theorem to find the length of the base (which is also the length of one side of the equilateral triangle).

Using the Pythagorean theorem: (base/2)^2 + (altitude)^2 = (side)^2

Substituting the given values: (base/2)^2 + (6√3)^2 = (side)^2

Simplifying this equation:

(base/2)^2 + 36*3 = side^2
(base/2)^2 + 108 = side^2

Now, since it is an equilateral triangle, all sides are equal, so we can write base = side.

Plugging in base = side, we have:
(side/2)^2 + 108 = side^2

Multiplying both sides by 4 to eliminate the fraction:
(side^2)/4 + 432/4 = side^2
(side^2 + 432)/4 = side^2

Cross multiplying, we get:
side^2 + 432 = 4 * side^2
4 * side^2 - side^2 = 432
3 * side^2 = 432
side^2 = 432/3
side^2 = 144

Taking the square root of both sides, we have:
side = √144
side = 12

Therefore, the length of one side of the equilateral triangle is 12 units.