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

The Correct Option is C

In a square, the diagonals are equal in length. So, \(4k + 6 = 7k - 3\).

\(3k = 9\)

\(k = 3\)

The length of a diagonal is \(4(3) + 6 = 12 + 6 = 18\) cm.

The area of a square is half the square of its diagonal: Area = \(\frac{1}{2} \times d^2\), where d is the diagonal

Area = \(\frac{1}{2} \times 18^2 = \frac{1}{2} \times 324 = 162\) cm²

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.