### Instruction: What is the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length 4 units to the numerical value of its perimeter, in units? Express your answer as a common fraction in simplest radical form.### Response: I know that the area of an equilateral triangle can be found by using the formula A = (s^2 sqrt{3})/4, where s is the side length.
So, for this triangle, the area is A = (4^2 sqrt{3})/4 = 4 sqrt{3} square units.
The perimeter of an equilateral triangle is just three times the side length, so for this triangle, the perimeter is P = 3(4) = 12 units.
The ratio of the area to the perimeter is then A/P = (4 sqrt{3})/12 = sqrt{3}/3.
This is already in simplest radical form, so I don't need to do anything else.