In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k - 3)$ cm. The area of the square (in cm2) is:
Answer & explanation
Correct answer: option 2
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