How many feet of chain fence are necessary to enclose a dog pen that is square and has an area of 64 sq feet?

To determine the amount of chain fence needed to enclose a square dog pen with an area of 64 square feet, we start by identifying the dimensions of the pen. The area of a square is calculated by squaring the length of one of its sides (Area = side × side).

Given that the area is 64 square feet, we can find the length of each side by taking the square root of 64. This results in a side length of 8 feet, since ( 8 × 8 = 64 ).

Next, to find the total length of the fence required to enclose the square pen, we calculate the perimeter. The perimeter of a square is calculated by adding all four sides together, or equivalently, by multiplying the length of one side by 4 (Perimeter = 4 × side).

Using the side length we found, the perimeter would be:

[ 4 × 8 = 32 \text{ feet} ]

Thus, the correct amount of chain fence necessary to enclose the pen is 32 feet. This confirms that the provided answer is indeed the appropriate choice for this question.