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GATE 2025 MA – Question 7

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

In the representative diagram QR ∥ ST. Their perpendicular separation is half the distance from P to QR. Find area(PST)/area(SQRT).

Diagram for GATE 2025 MA question 7
  1. 1/3
  2. 1/4
  3. 2/5
  4. 1/2

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Show answer and explanation

Correct answer: (A) 1/3

Explanation

The height from P to ST is half the height from P to QR. Similarity gives linear ratio 1/2, so PST has 1/4 of PQR’s area and the trapezium has 3/4. Ratio = (1/4)/(3/4) = **1/3, A**.

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