Question

What is the area of a square? Statement I: The perimeter of the square is 20 cm. Statement II: The diagonal of the square is \(\sqrt{50}\) cm.

• A. Statement I alone is sufficient, but Statement II alone is not sufficient.
• B. Statement II alone is sufficient, but Statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Hint:

Recall that a square's area can be written directly in terms of its perimeter (Area = P squared over 16) or directly in terms of its diagonal (Area = d squared over 2), without solving for the side first.

Answer 1

The Correct Option is D

Statement I: perimeter 20 \(\Rightarrow\) side \(=5\) \(\Rightarrow\) area \(=25\) cm\(^2\); sufficient. Statement II: diagonal \(\sqrt{50}\) \(\Rightarrow\) side\(^2\times 2=50\Rightarrow\) side\(^2=25\Rightarrow\) area \(=25\) cm\(^2\); sufficient. Each statement alone gives the area. Correct option: Each statement alone is sufficient.