Final answer:
To find the length of BD in the square rubber mat, we divide the perimeter by 4 to find the length of each side. Then, we can use the Pythagorean theorem to find the length of the diagonal BD, which is 12√2 units.
Step-by-step explanation:
To find the length of BD, we need to consider that the mat is a square. The perimeter of a square is calculated by adding up all its sides. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side. In this case, the perimeter is 48 units, so each side is 48 / 4 = 12 units long.
Since BD is a diagonal of the square, we can use the Pythagorean theorem to find its length. The sides of a square and the diagonal form a right triangle. Let's call the length of one side of the square x. Using the Pythagorean theorem, we have:
x^2 + x^2 = BD^2
2x^2 = BD^2
BD = √(2x^2)
BD = √(2 * 12^2)
BD = √(2 * 144)
BD = √288
BD = 12√2 units