The GATE Grind

GATE 2025 CS (CS1) – Question 7

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

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 S on PQ and T on PR, and ST parallel to QR.
  1. $\frac{1}{3}$
  2. $\frac{1}{4}$
  3. $\frac{2}{5}$
  4. $\frac{1}{2}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\frac{1}{3}$

Explanation

ST is at height h/2 from QR, so P is at h/2 from ST. Then PST ~ PQR with ratio 1/2, so area(PST)=1/4 of PQR and the trapezium is 3/4. The required ratio is 1/3.