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
The two diagonals of a square are equal, so the two expressions are set equal to find k. The area of a square from its diagonal d is \(\frac{d^{2}}{2}\), because the square is two right triangles, each with base d and height \(\frac{d}{2}\).
Equal diagonals: \(4k+6=7k-3\), so \(3k=9\) and \(k=3\)
So each diagonal \(=4\times3+6=18\,\mathrm{cm}\)
Area of the square \(\displaystyle =\frac{18^{2}}{2}=\frac{324}{2}=162\,\mathrm{cm^2}\)