यदि ∆ ABC ~ ∆DEF इस प्रकार है कि 2AB = DE और BC = 8 सेमी है, तो EF की लंबाई क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 2)
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  1. 16 सेमी 
  2. 18 सेमी 
  3. 22 सेमी 
  4. 20 सेमी 

Answer (Detailed Solution Below)

Option 1 : 16 सेमी 
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दिया गया:

∆ ABC ~ ∆DEF

2AB = DE

BC = 8 सेमी

प्रयुक्त अवधारणा:

समरूप त्रिभुज की संगत भुजाओं का अनुपात बराबर होता है

गणना:

∆ ABC ~ ∆DEF के रूप में 

⇒ \(\frac{AB}{DE}=\frac{BC}{EF}\)

जैसा कि हम जानते हैं, 2AB = DE

⇒ \(\frac{AB}{2AB}=\frac{8}{EF}\)

⇒  ईएफ = 8 \(\times\) 2 = 16 सेमी

⇒ अत:, EF का मान 16 सेमी है।

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