GATE 2022 EC – Question 3
A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
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Show answer and explanation
Correct answer: (B) 2.40
Explanation
The parallel sides differ by $11-6=5$ cm. Sliding the leg SP along so that it meets QR forms a triangle with sides $3,4,5$, which is right-angled. The height of the trapezium is the altitude to the hypotenuse, $\frac{3\times4}{5}=2.4$ cm.