Question

an equilateral triangle has a perimeter of (15x^3 + 33x^5) feet. what is the length of each side?
( circ ) (x^3) feet
( circ ) (5 + 11x^2) feet
( circ ) (5x^2 + 11) feet
( circ ) (5x^3 + 11x^5) feet

Explanation:

Step1: Recall perimeter of equilateral triangle

An equilateral triangle has three equal sides. So, the length of each side is the perimeter divided by 3. The perimeter \( P = 15x^{3}+33x^{5} \). So, each side length \( s=\frac{15x^{3} + 33x^{5}}{3} \).

Step2: Divide each term by 3

Using the distributive property of division over addition, \( \frac{15x^{3}+33x^{5}}{3}=\frac{15x^{3}}{3}+\frac{33x^{5}}{3} \).

Step3: Simplify each term

Simplify \( \frac{15x^{3}}{3}=5x^{3} \) and \( \frac{33x^{5}}{3} = 11x^{5} \). So, \( s = 5x^{3}+11x^{5} \) feet.

Answer:

\( 5x^{3}+11x^{5} \) feet (corresponding to the option " \( 5x^{3}+11x^{5} \) feet")