Question

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

Explanation:

Step1: Recall the property of an equilateral triangle

In an equilateral triangle, all three sides are equal. Let the length of each side be \(s\). The perimeter \(P\) of a triangle is \(P = 3s\). Given \(P=15x^{3}+33x^{5}\), then \(s=\frac{15x^{3}+33x^{5}}{3}\).

Step2: Divide each term in the numerator by 3

Using the rule \(\frac{a + b}{c}=\frac{a}{c}+\frac{b}{c}\) (\(c
eq0\)), we have \(\frac{15x^{3}+33x^{5}}{3}=\frac{15x^{3}}{3}+\frac{33x^{5}}{3}\).
For \(\frac{15x^{3}}{3}\), since \(15\div3 = 5\), then \(\frac{15x^{3}}{3}=5x^{3}\).
For \(\frac{33x^{5}}{3}\), since \(33\div3=11\), then \(\frac{33x^{5}}{3}=11x^{5}\).

Answer:

\(5x^{3}+11x^{5}\) feet (the fourth option).