joan is building a sandbox in the shape of a regular pentagon. the perimeter of the pentagon is…

joan is building a sandbox in the shape of a regular pentagon. the perimeter of the pentagon is $35y^{4}-65x^{3}$ inches. what is the length of one side of the sandbox?\n$5y - 9$ inches\n$5y^{4}-9x^{3}$ inches\n$7y - 13$ inches\n$7y^{4}-13x^{3}$ inches

joan is building a sandbox in the shape of a regular pentagon. the perimeter of the pentagon is $35y^{4}-65x^{3}$ inches. what is the length of one side of the sandbox?\n$5y - 9$ inches\n$5y^{4}-9x^{3}$ inches\n$7y - 13$ inches\n$7y^{4}-13x^{3}$ inches

Answer

Explanation:

Step1: Recall the perimeter formula for a regular pentagon

A regular pentagon has 5 equal - length sides. Let the length of one side be $s$. The perimeter $P = 5s$.

Step2: Solve for the side - length

We know that $P=35y^{4}-65x^{3}$. Since $P = 5s$, then $s=\frac{P}{5}$. [ \begin{align*} s&=\frac{35y^{4}-65x^{3}}{5}\ &=\frac{35y^{4}}{5}-\frac{65x^{3}}{5}\ & = 7y^{4}-13x^{3} \end{align*} ]

Answer:

D. $7y^{4}-13x^{3}$ inches