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GATE 2025 CS (CS2) – Question 9

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

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: The figure shown is representative.

square PQRS with rectangle PLMN tilted so that L lies on QR and side MN passes through S.
  1. $2\sqrt{2}$
  2. $2$
  3. $8$
  4. $4$

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Correct answer: (D) $4$

Explanation

Triangle PLS has base PL and height equal to PN (S lies on MN, which is parallel to PL), so its area is half the rectangle. The same triangle has base PS = 2 and height 2 (L is on QR), so its area is 2. The rectangle's area is 4.