Final answer:
The length of the diagonal of the square playground is 60√2 yards.The correct answer is option A. 60√2 yd.
Step-by-step explanation:
To find the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.
Since a square has four equal sides, the perimeter of the square is 120 yards. Therefore, each side of the square is 120/4 = 30 yards.
Let's represent the length of the diagonal as d. Using the Pythagorean theorem, we can set up the equation: d^2 = 30^2 + 30^2. Simplifying this equation, we get: d^2 = 2(30^2). Taking the square root of both sides, we find that d = sqrt(2(30^2)) = 30√2 yards.
Therefore, the length of the diagonal of the square playground is 60√2 yards, which corresponds to option A.