Question
Download Solution PDFसमरूप त्रिभुज ΔPQR और ΔDEF की भुजाएं 5 ∶ 6 के अनुपात में हैं। यदि ΔPQR का क्षेत्रफल 75 सेमी2 के बराबर है तो ΔDEF का क्षेत्रफल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
ΔPQR ∼ ΔDEF
ΔPQR और ΔDEF की भुजाएं 5 ∶ 6 के अनुपात में हैं।
क्षेत्रफल(PQR) = 75 सेमी2
प्रयुक्त सूत्र:
समरूप त्रिभुजों के क्षेत्रफलों का अनुपात संगत त्रिभुजों की भुजाओं के अनुपात के वर्ग के बराबर होता है।
गणना:
ΔPQR ∼ ΔDEF
क्षेत्रफल(PQR)/क्षेत्रफल(DEF) = (ΔPQR की भुजा/ΔDEF की भुजा)2
⇒ 75/क्षेत्रफल(DEF) = (5/6)2
⇒ क्षेत्रफल(DEF) = 108 सेमी2
∴ ΔDEF का क्षेत्रफल 108 सेमी2 के बराबर है।
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