GATE CS 2025 Set 2 | Question 9

MCQ · 2 marks · −0.66

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 at the top left, S at the top right, R at the bottom right and Q at the bottom left. A tilted rectangle PLMN shares corner P with the square, has corner L on side QR, and its side MN passes through S, with N above the square and M to its right.
  1. Option A: \(2\sqrt{2}\)
  2. Option B: 2
  3. Option C: 8
  4. Option D: 4 (correct)

Answer

(D)

Explanation

Find the area of triangle PLS in two ways.

  • With base PS: PS = 2 cm, and L lies on QR, which is 2 cm from PS. So the area is \(\frac{1}{2} \times 2 \times 2 = 2\) cm2.
  • With base PL: S lies on MN, which is parallel to PL at a distance LM. So the area is \(\frac{1}{2} \times PL \times LM\), half the rectangle.

Hence the rectangle’s area is \(2 \times 2 = 4\) cm2, wherever L sits on QR.

Answer: D