पूर्णांक मानों की भुजाओं वाले त्रिभुज का परिमाप 13 के बराबर है। ऐसे कितने त्रिभुज सम्भव हैं?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 3)
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  1. 5
  2. 8
  3. 7
  4. 6

Answer (Detailed Solution Below)

Option 1 : 5
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प्रयुक्त अवधारणा:

यदि त्रिभुज का परिमाप "p" है

माना कुल सम्भावित त्रिभुज "t" है।

यदि p = सम है, तो

t = p2/48

यदि = विषम है, तो

t = (p + 3)2/48

गणना:

प्रश्नानुसार,

कुल सम्भावित त्रिभुज = (13 + 3)2/48

⇒ 5.33 ≈ 5

∴ कुल सम्भावित त्रिभुज 5 हैं।

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