Question

finding the length

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?

• \\(5y - 9\\) inches
• \\(5y^4 - 9x^3\\) inches
• \\(7y - 13\\) inches
• \\(7y^4 - 13x^3\\) inches

Explanation:

Identify the geometric relationship

$$ \text{Perimeter of a regular pentagon} = 5 \times \text{side length} $$

Set up the division equation

$$ \text{Side length} = \frac{\text{Perimeter}}{5} = \frac{35y^4 - 65x^3}{5} $$

Divide each term by the constant

$$ \text{Side length} = \frac{35y^4}{5} - \frac{65x^3}{5} = 7y^4 - 13x^3 $$

Answer:

• (A) \(5y - 9\) inches
• (B) \(5y^4 - 9x^3\) inches
• (C) \(7y - 13\) inches
• (D) \(7y^4 - 13x^3\) inches (Correct answer)