Question
Download Solution PDFयदि ∆ABC ~ ∆DEF, और BC = 4 सेमी, EF = 5 सेमी और त्रिभुज ABC का क्षेत्रफल = 80 सेमी2 है, तो त्रिभुज DEF का क्षेत्रफल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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।
Last updated on Jul 8, 2025
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