The diagonal of a square is not equal to its sides; in fact, it is longer than each side. To understand why this is the case, let’s consider the properties of a square.
A square is a quadrilateral with all four sides of equal length and all four angles measuring 90 degrees. When you draw a diagonal, it connects two non-adjacent corners of the square. This diagonal effectively divides the square into two right-angled triangles.
To calculate the length of the diagonal (
the line segment that connects two opposite corners) in relation to the sides, we can apply the Pythagorean theorem. If we denote the length of each side of the square as s, the diagonal d can be calculated using the equation:
d = √(s² + s²)
= √(2s²)
= s√2
This result shows that the diagonal is equal to the length of a side multiplied by the square root of 2 (approximately 1.414). So, if you think about it, the diagonal is about 41.4% longer than each side of the square. As an example, if the side length of a square is 1 unit, the diagonal would measure about 1.414 units.
In summary, the diagonal of a square is always longer than its sides, precisely calculated by the formula d = s√2. This relationship is fundamental in geometry and can be visually confirmed by measuring actual squares.