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GATE CH 2023 | GA Question: 3

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

  1. $\frac{20}{7}$
  2. $\frac{28}{5}$
  3. $\frac{9}{2}$
  4. $\frac{35}{4}$
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In the above figure,

Area of a parallelogram = base x height

Taking QR as base and PT as height

Area of parallelogram = QR X PT

                                  = 7 x 4  ------- 1

Taking RS as base and PV as height

Area of a parallelogram = RS X PV

                                      = RS x 5  -------- 2

Equating 1 and 2,

7 x4 = RS x 5

 28 = RS x 5

RS = 28/5
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