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GATE 2022 MT – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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)?

  1. 1.80
  2. 2.40
  3. 4.20
  4. 5.76

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Show answer and explanation

Correct answer: (B) 2.40

Explanation

The base-length difference is 5 cm. Let the leg projections be $x$ and $5-x$. Equal squared heights require $9-x^2=16-(5-x)^2$, giving $x=1.8$.

Hence $h=\sqrt{9-1.8^2}=2.40$ cm, **B**.