Final answer:
The expression that represents the length of one side of an equilateral triangle's perimeter is P/3, where P is the total perimeter. It is derived by dividing the total perimeter by the three equal sides of the triangle.
Step-by-step explanation:
The question pertains to identifying the expression that represents the length of one side of an equilateral triangle's perimeter. In an equilateral triangle, all sides are of equal length. Therefore, to find the length of one side, we can divide the total perimeter by the number of sides. The total perimeter (P) divided by the number of sides (3, in the case of an equilateral triangle) gives us the length of one side. Therefore, the correct expression is P/3, where P is the total perimeter of the equilateral triangle.
Considering other options: P - 2s (option b) does not yield the length of one side because subtracting two times a side from the total perimeter doesn't equal the length of one side. Option c, P/4, would be appropriate for a square, not an equilateral triangle. Option d, 3s, represents three times the length of a side, which is the perimeter itself.
An analogous concept can be found when discussing squares. The perimeter of a square can be found by multiplying the side length (a) by 4, giving 4a, since a square has four equal sides.
The Pythagorean theorem relates the sides of a right triangle but is not directly relevant to finding the length of a side of an equilateral triangle from its perimeter.