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A farmer is building a pentagon (that is, 5-sided) pen to hold his animals. Each side has an equal length. What is the total perimeter of the pen if the length of one side is [tex]$3 \sqrt{5}$[/tex] yards?

A. [tex]$8 \sqrt{5}$[/tex] yards
B. [tex][tex]$15 \sqrt{5}$[/tex][/tex] yards
C. [tex]$8 \sqrt{25}$[/tex] yards
D. [tex]$15 \sqrt{25}$[/tex] yards


Sagot :

To find the total perimeter of the pentagon-shaped chicken pen, we need to understand that the perimeter of any polygon is the sum of the lengths of all its sides.

In this case, the pentagon has 5 equal sides, and each side is [tex]\(3\sqrt{5}\)[/tex] yards long.

To calculate the perimeter, we multiply the length of one side by the number of sides.

Let's break it down step by step:

1. Identify the length of one side:
The length of one side is [tex]\(3\sqrt{5}\)[/tex] yards.

2. Calculate the number of sides:
A pentagon has 5 sides.

3. Multiply the length of one side by the number of sides:
[tex]\[ \text{Perimeter} = 5 \times 3\sqrt{5} \][/tex]

4. Perform the multiplication:
[tex]\[ \text{Perimeter} = 15\sqrt{5} \text{ yards} \][/tex]

Therefore, the total perimeter of the chicken pen is [tex]\(15\sqrt{5}\)[/tex] yards.

Thus, the correct answer is:
B. [tex]\(15\sqrt{5}\)[/tex] yards