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GATE CSE 2025 Session 1 Q7: Ratio of triangle PST to trapezium SQRT

Question

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?

Note: The figure shown is representative.

Triangle PQR with apex P at the top and base QR; segment ST parallel to QR joins S on PQ and T on PR
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Answer: A (official GATE 2025 final answer key)

Concept used: Similar triangles: areas scale as the square of the ratio of corresponding lengths.

First step: ST is halfway between P and QR, so triangle PST is similar to PQR with ratio 12\tfrac{1}{2} and has 14\tfrac{1}{4} of its area.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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