A square has side lengths measuring 9 centimeters each. What is the length of the line connecting two opposite vertices of the square?

To find the length of the diagonal connecting two opposite vertices of a square, you can use the Pythagorean theorem. For a square with side length \(s\), the diagonal \(d\) is given by the formula \(d = s\sqrt{2}\). In your case, substituting \(s = 9\) cm, you get: \(d = 9\sqrt{2} \approx 12.73\) cm. So, the length of the diagonal is approximately 12.73 centimeters! Did you know that the concept of the square diagonal has been around since ancient Greek mathematicians like Pythagoras? They explored properties of triangles and squares, paving the way for geometry as we know it. This diagonal not only connects vertices but also has fun connections to various fields like architecture and art, where symmetry is key.