Final answer:
To find the side length of an equilateral triangle with an area of 8 square root 3, use the formula for the area of an equilateral triangle, solve for the side length, and find that it is 4 square root 2 units.
Step-by-step explanation:
To find the length of a side of an equilateral triangle with an area of 8 square root 3 square units, we use the formula for the area of an equilateral triangle, which is A = (sqrt(3)/4) × a², where A is the area and a is the length of a side.
Given that the area A is 8√3, we can set up the equation as follows:
8√3 = (sqrt(3)/4) × a².
Now, we solve for a²:
a² = (8√3) × (4/sqrt(3)).
By simplifying, we get a² = 32,
so a = √32.
Thus, the length of one side of the triangle is
a = √sqrt(32)
= 4√2 units.