Final answer:
To find the length of the diagonal of a square enclosure with a perimeter of 16 feet, divide the perimeter by 4 to find the length of one side. Then, use the Pythagorean theorem to calculate the length of the diagonal.
Step-by-step explanation:
To find the length of the diagonal of a square enclosure, we need to first calculate the length of one side of the square. The given information tells us that the perimeter of the square is 16 feet. Since a square has four equal sides, we can divide the perimeter by 4 to find the length of one side. 16 feet ÷ 4 = 4 feet.
Next, we can use the length of one side to find the length of the diagonal. In a square, the diagonal forms a right triangle with two sides that are equal to the length of one side. Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
Diagonal^2 = Side^2 + Side^2
Diagonal^2 = 4^2 + 4^2
Diagonal^2 = 16 + 16
Diagonal^2 = 32
Diagonal = √32
Diagonal ≈ 5.66 feet