No, the diagonal of a square is not equal to its sides. In fact, the diagonal is longer than each side of the square.
To understand why this is the case, let’s take a closer look at a square. A square has four equal sides, and if we label the length of each side as ‘s’, we can derive the length of the diagonal using the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (d, the diagonal) is equal to the sum of the squares of the lengths of the other two sides (which are both ‘s’ for a square). Thus, we can express this relationship as:
d² = s² + s²
This simplifies to:
d² = 2s²
Taking the square root of both sides gives us:
d = s√2
This means that the diagonal d is approximately 1.414 times the length of the sides s, which clearly shows that the diagonal is longer than the sides. Therefore, while all sides of a square are equal, the diagonal is not equal to them; it is actually a bit longer.