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# Is the diagonal of a square equal to its sides?

A square is a closed two-dimensional figure with four sides and four corners. The length of all four sides is equal and angles at the corners are right-angles.

## Answer: No, the diagonal of a square is not equal to its sides.

The diagonal of a square is calculated by using the formula: Diagonal of Square (d) = √2 × s, Here 's' is the side of the square.

**Explanation:**

The following image shows a square ABCD with diagonals, AC and BD

The diagonal formula is calculated by using the Pythagoras Theorem.

Consider a square ABCD with sides AB = BC = CD = AD = s and diagonals AC = BD = d. Since the angles at the corners of the square are right angles, we have

AC^{2} = AD^{2} + CD^{2}

d^{2} = (s^{2 }+ s^{2})

= 2s^{2}

d = √2 × s

So, Diagonal of Square (d) = √2 × s, where s is the length of each side of the square.

### Therefore, the diagonal of a square is not equal to its sides.

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