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GATE 2025 IN – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

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

Diagram for GATE 2025 IN question 9
  1. $2\sqrt2$
  2. 2
  3. 8
  4. 4

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Show answer and explanation

Correct answer: (D) 4

Explanation

Use P=(0,2), Q=(0,0), R=(2,0), S=(2,2), and L=(a,0). The rectangle length PL is √(a²+4). Its width is the perpendicular distance from S to PL, namely 4/√(a²+4). Their product is **4 cm², D**, independent of L.