The diagonal of a square is 60 cm. Calculate its peremeter

To find the perimeter of a square, we need to know the length of one of its sides. Let's call the length of one side of the square "x". Since the square has four equal sides, we can say that the perimeter of the square is equal to 4 times x, or 4x. We are given that the diagonal of the square is 60 cm. We know that the diagonal of a square forms a right triangle with two sides that are equal to the length of one side of the square. We can use the Pythagorean theorem to find the length of one side of the square. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the diagonal of the square, which we know is 60 cm. We can let one side of the square be "x", as we mentioned earlier. The other side of the square is also "x" because the square has four equal sides. So we have: 60^2 = x^2 + x^2 Simplifying this equation, we get: 3600 = 2x^2 Dividing both sides by 2, we get: 1800 = x^2 Taking the square root of both sides, we get: x = sqrt(1800) We can simplify this answer by factoring out the square of a perfect square: x = sqrt(900 * 2) x = sqrt(900) * sqrt(2) x = 30 * sqrt(2) Now that we know the length of one side of the square, we can find its perimeter by multiplying by 4: perimeter = 4x = 4(30 * sqrt(2)) = 120 * sqrt(2) Therefore, the answer is 120\(\sqrt{2}\).