To find the length of each side of an equilateral triangle when given its perimeter, we need to understand a key property of equilateral triangles: all three sides are of equal length. Therefore, the perimeter of an equilateral triangle is three times the length of one side.
Let's denote the perimeter as [tex]\( P \)[/tex].
[tex]\[ P = 15x^3 + 33x^5 \][/tex]
Since the triangle is equilateral, the length of each side [tex]\( s \)[/tex] can be calculated by dividing the perimeter by 3:
[tex]\[ s = \frac{P}{3} \][/tex]
Now, let's substitute [tex]\( P = 15x^3 + 33x^5 \)[/tex] into the equation:
[tex]\[ s = \frac{15x^3 + 33x^5}{3} \][/tex]
To divide each term in the numerator by 3, we perform the division individually for each term:
[tex]\[ s = \frac{15x^3}{3} + \frac{33x^5}{3} \][/tex]
[tex]\[ s = 5x^3 + 11x^5 \][/tex]
Thus, the length of each side of the equilateral triangle is:
[tex]\[ 5x^3 + 11x^5 \][/tex]
So, the correct answer is:
[tex]\[ 5x^3 + 11x^5 \][/tex] feet
