The problem states that an equilateral triangle has three sides of equal length. The function $P$ gives the perimeter of an equilateral triangle with side length $s$. We need to find $P(2)$, $P(10)$, and $P(s)$.

1. Problem Description

The problem states that an equilateral triangle has three sides of equal length. The function $P$ gives the perimeter of an equilateral triangle with side length $s$. We need to find $P(2)$, $P(10)$, and $P(s)$.

2. Solution Steps

Since the triangle is equilateral, all three sides have the same length, $s$.

The perimeter $P$ is the sum of the lengths of the three sides.

Therefore, $P(s) = s + s + s = 3s$.

a. To find $P(2)$, we substitute $s=2$ into the formula for $P(s)$.

$P(2) = 3(2) = 6$

b. To find $P(10)$, we substitute $s=10$ into the formula for $P(s)$.

$P(10) = 3(10) = 30$

c. To find $P(s)$, we already derived the formula:

$P(s) = 3s$

3. Final Answer

a. $P(2) = 6$

b. $P(10) = 30$

c. $P(s) = 3s$