Question

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

Explanation:

Step1: Recall equilateral - triangle property

In an equilateral triangle, perimeter \(P = 3s\), where \(s\) is the length of each side. So, \(s=\frac{P}{3}\).

Step2: Divide the given perimeter by 3

Given \(P = 15x^{3}+33x^{5}\), then \(s=\frac{15x^{3}+33x^{5}}{3}\).
Using the distributive property of division \(\frac{a + b}{c}=\frac{a}{c}+\frac{b}{c}\), we have \(s=\frac{15x^{3}}{3}+\frac{33x^{5}}{3}\).
\(\frac{15x^{3}}{3}=5x^{3}\) and \(\frac{33x^{5}}{3}=11x^{5}\), so \(s = 5x^{3}+11x^{5}\).

Answer:

\(5x^{3}+11x^{5}\text{ feet}\)