यदि ∆ABC ~ ∆DEF, और BC = 4 सेमी, EF = 5 सेमी और त्रिभुज ABC का क्षेत्रफल = 80 सेमी2 है, तो त्रिभुज DEF का क्षेत्रफल क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 4)
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  1. 169 सेमी2
  2. 80 सेमी2
  3. 144 सेमी2
  4. 125 सेमी2

Answer (Detailed Solution Below)

Option 4 : 125 सेमी2
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दिया गया:

∆ABC ~ ∆DEF, और BC = 4 सेमी, EF = 5 सेमी और त्रिभुज ABC का क्षेत्रफल = 80 सेमी²

प्रयुक्त अवधारणा:

दो समरूप त्रिभुजों में, 

उनके क्षेत्रफल का अनुपात उनकी संगत भुजाओं के वर्गों के अनुपात के बराबर होता है।

गणना:

प्रश्न के अनुसार,

∆ABC का क्षेत्रफल : ∆DEF का क्षेत्रफल = BC² : EF²

⇒80 : ∆DEF का क्षेत्रफल = 4² : 5²

⇒∆DEF का क्षेत्रफल = 25 × 80/16

⇒∆DEF का क्षेत्रफल = 125

इसलिए, अभीष्ट मान 125 सेमी² है।

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