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GATE CSE 2025 Session 2 Q9: Area of a rectangle PLMN drawn on a square PQRS

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 cm²) of the rectangle PLMN?

Note: The figure shown is representative.

Square PQRS with P top-left, Q bottom-left, R bottom-right, S top-right; rectangle PLMN with L on QR and side MN passing through S
Tap the figure to enlarge

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Answer: D (official GATE 2025 final answer key)

Concept used: A triangle and a rectangle on the same base and between the same parallels: the triangle is half the rectangle.

First step: Triangle PLSPLS has base PLPL and its apex SS on MNMN, so its area is half of PLMN; it is also half of the square (base PSPS, height 2).

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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