No, the diagonal of a square is not the same length as the side.
To understand why, let’s consider a square with each side measuring a. The diagonal can be calculated using the Pythagorean theorem. In a square, the diagonal d connects two opposite corners, forming a right triangle with two sides of the square.
According to the Pythagorean theorem:
d = √(a² + a²)
Simplifying this gives:
d = √(2a²) = a√2
This shows that the diagonal is approximately 1.414 times the length of one side (since √2 is about 1.414). Therefore, the diagonal of a square is longer than each of its sides.