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PQRS is a parallelogram, PX ⊥ SR and RY ⊥ PS. If PQ = 21 cm, PX = 8 cm and RY = 12 cm, find PS. 

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  1. 14 cm
  2. 13 cm
  3. 16 cm
  4. 15 cm

Answer (Detailed Solution Below)

Option 1 : 14 cm
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Detailed Solution

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Given:

PQRS is a parallelogram

PQ = 21 cm

PX ⟂ SR

RY ⟂ PS

PX = 8 cm

RY = 12 cm

Formula used:

Area of parallelogram = Base × Height

Calculation:

Area using PQ and PX:

Area = PQ × PX

⇒ Area = 21 cm × 8 cm

⇒ Area = 168 cm2

Area using PS and RY:

Area = PS × RY

⇒ 168 cm2 = PS × 12 cm

⇒ PS = 168 cm2 ÷ 12 cm

⇒ PS = 14 cm

∴ The correct answer is option (1).

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