Question

In the given figure, PQRS is a square of side 2 cm, and PLMN is a rectangle. The corner \( L \) of the rectangle is on the side \( QR \). Side \( MN \) of the rectangle passes through the corner \( S \) of the square. What is the area (in cm\(^2\)) of the rectangle PLMN? Note: 

• A. \( 2\sqrt{2} \)
• B. \( 2 \)
• C. \( 8 \)
• D. \( 4 \)

Hint:

When solving geometry-based problems in GATE, visualize the problem by sketching the given conditions and applying coordinate geometry or transformations to derive unknown dimensions.

Answer 1

The Correct Option is D

Given that PQRS is a square of side 2 cm, and the rectangle PLMN is oriented such that it extends through the square's corner, we analyze its dimensions.

To solve this, we begin by understanding the relationship between the square and the rectangle. The square PQRS has a side length of 2 cm, and the rectangle PLMN is positioned such that it extends through one of the square's corners. The geometric arrangement of the rectangle within the square gives us the area of the rectangle.

Through geometric analysis, we calculate that the area of the rectangle PLMN is \( 4 \, \text{cm}^2 \), derived from the given dimensions and the square's configuration. The placement of the rectangle ensures that its area is directly tied to the side length of the square, and hence the result is straightforward.

Thus, the correct answer is (D).