Gate CS 2025 (CS1)| Question - 7 | General Aptitude

April 04, 2025

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.

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{2}{5}$

$\frac{1}{2}$

Solution:

There is a theorem

$∴ \frac{1}{2} Q R = S T \frac{Δ P S T}{□ S T Q R} = \frac{\frac{1}{2} [S T] h}{\frac{1}{2} h (S T + Q R))} = \frac{S T}{S T + Q R} = \frac{S T}{S T + 2 S T} = \frac{S T}{3 S T} = \frac{1}{3}$

Gate CS 2025 (CS1)| Question - 7 | General Aptitude

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