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A square playground has a perimeter of 120 yards. What is the length of a diagonal of the playground?

A. 60√2 yd
B. 90√2 yd
C. 45 yd
D. 30√2 yd

User Jmbmage
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1 Answer

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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.

User Ctacke
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