एक इष्टिकाचितीची लांबी, रुंदी आणि उंची यांची बेरीज 8 सेमी आहे आणि त्याचा कर्ण 5 सेमी आहे. तर त्याचे पृष्ठफळ काय असेल?

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RPF Constable 2024 Official Paper (Held On 03 Mar, 2025 Shift 1)
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  1. 39 सेमी2
  2. 64 सेमी2
  3. 25 सेमी2
  4. 89 सेमी2

Answer (Detailed Solution Below)

Option 1 : 39 सेमी2
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Detailed Solution

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दिलेले आहे:

लांबी + रुंदी + उंची = 8 सेमी

कर्ण = 5 सेमी

वापरलेले सूत्र:

कर्ण2 = l2 + w2 + h2

पृष्ठफळ = 2 × (lw + wh + hl)

गणना:

समजा, l + w + h = 8 ...(i)

⇒ कर्ण2 = 52 = 25

l2 + w2 + h2 = 25 ...(ii)

आता, (l + w + h)2 = l2 + w2 + h2 + 2(lw + wh + hl)

⇒ 82 = 25 + 2(lw + wh + hl)

⇒ 64 = 25 + 2(lw + wh + hl)

⇒ 2(lw + wh + hl) = 39

⇒ lw + wh + hl = 19.5

पृष्ठफळ = 2 × 19.5 = 39 सेमी2

∴ पृष्ठफळ 39 सेमी2 असेल.

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