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GATE 2023 MT – Question 3

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

PQRS is a parallelogram with PS = 7 cm, PT = 4 cm, and PV = 5 cm, as shown. PT and PV are perpendicular to QR and RS, respectively. What is RS in cm? The diagram is representative.

Diagram for GATE 2023 MT question 3
  1. $20/7$
  2. $28/5$
  3. $9/2$
  4. $35/4$

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Show answer and explanation

Correct answer: (B) $28/5$

Explanation

The parallelogram area is $PS\times PT=7(4)=28$ cm$^2$. Using the alternative base and height gives $RS\times PV=5RS$.

Therefore $RS=28/5$ cm, **B**.