Final answer:
To estimate the side length of a square with a 9 cm long diagonal, we can use the Pythagorean theorem. The estimated side length of the square is approximately 6.36 cm.
Step-by-step explanation:
To estimate the side length of a square with a 9 cm long diagonal, we can use the Pythagorean theorem. 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 other two sides. In this case, the diagonal of the square is the hypotenuse, and the two sides of the square are the same length.
Let's assume that the side length of the square is x cm. According to the Pythagorean theorem, we have x2 + x2 = 92. Simplifying, we get 2x2 = 81. Dividing both sides by 2, we get x2 = 40.5. Taking the square root of both sides, we find x ≈ 6.36 cm.
Therefore, the estimated side length of the square is approximately 6.36 cm.
Learn more about Estimating the side length of a square with a given diagonal