If sum of lengths of the diagonals of a square is 24 cm, then what is the length of the side of the square?

$6 \sqrt{2}$ cm

We have,

Sum of lengths of the diagonals of a square = 24 cm

We know that,

length of the diagonal of the square is equal.

So, each diagonal = 12cm

Now, diagonal of the square = side × \(\sqrt {2}\)

= 12 / \(\sqrt {2}\) = side

side = $6 \sqrt{2}$ cm