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GATE 2023 CH – Question 3

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

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

a parallelogram PQRS with PS = 7 cm along the top, PT = 4 cm the perpendicular from P to the side QR (foot T), and PV = 5 cm the perpendicular from P to the side RS extended (foot V).
  1. $\frac{20}{7}$
  2. $\frac{28}{5}$
  3. $\frac{9}{2}$
  4. $\frac{35}{4}$

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Show answer and explanation

Correct answer: (B) $\frac{28}{5}$

Explanation

The area of the parallelogram can be found in two ways. With the base QR = PS = 7 cm and the height PT = 4 cm, the area is $7 \times 4 = 28$ cm². With the base RS and the height PV = 5 cm, the area is $5 \times RS$. So $RS = \frac{28}{5}$ cm.