एक आयत की लंबाई और चौड़ाई का अनुपात 5:3 है। वृत्त का व्यास, आयत की लंबाई का 7/5 है। वृत्त की परिधि, आयत के परिमाप से 24 मीटर अधिक है। आयत का क्षेत्रफल ज्ञात कीजिए। 

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RRB PO Prelims Memory Based Paper (Held On: 4 August 2024 Shift 1)
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  1. 340
  2. 280
  3. 216
  4. 240
  5. 220

Answer (Detailed Solution Below)

Option 4 : 240
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गणना

माना, लंबाई = 5x, चौड़ाई = 3x
वृत्त का व्यास = (7/5) × 5x = 7x
⇒ त्रिज्या = 7x/2
परिधि = 2πr = 2 × (22/7) × (7x/2) = 22x

आयत का परिमाप = 2(5x + 3x) = 16x
दिया गया है:
22x = 16x + 24
⇒ 6x = 24 ⇒ x = 4

लंबाई = 20, चौड़ाई = 12
क्षेत्रफल = 20 × 12 = 240 मीटर²

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