Question

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

• A. 144
• B. 162
• C. 169
• D. 172

Answer 1

Answer: (C)

169

Answer 2

Since the diagonals of a square are equal, $4k + 6 = 7k - 3 \Rightarrow 3k = 9 \Rightarrow k = 3$. The diagonal is $4 \times 3 + 6 = 18$ cm. The area of the square is $\frac{1}{2} \times 18^2 = 162$ cm².