In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k - 3)$ cm. The area of the square (in cm²) is:

162

The correct answer is Option (2) → 162

We know that length of the two diagonals of a square is always equal.

Therefore,

4K + 6 = 7K - 3

7K - 4K = 6 + 3 = 9

K = 3

Now, length of Diagonal = 4K + 6 = 12 + 6 = 18 cm

Length of Diagonal of square = \(\sqrt {2}\)side = 18

Side of square = \(\frac{18}{\sqrt {2}}\) = 9\(\sqrt {2}\)

Now,

Area of square = (side)² = {9\(\sqrt {2}\)}² = 162