Question
Download Solution PDFΔABC ~ ΔPQR, ΔABC और ΔPQR के क्षेत्रफल क्रमशः 64 सेमी2 और 81 सेमी2 हैं और AD और PT क्रमशः ΔABC और ΔPQR की माध्यिकाएं हैं। यदि PT = 10.8 सेमी, तो AD = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
ΔABC ~ ΔPQR
ΔABC का क्षेत्रफल = 64 सेमी2
ΔPQR का क्षेत्रफल = 81 सेमी2
PT = 10.8 सेमी
AD, ΔABC की माध्यिका है।
PT, ΔPQR की माध्यिका है।
अवधारणा:
दो समरूप त्रिभुजों के क्षेत्रफलों का अनुपात संगत भुजाओं और माध्यिकाओं के वर्गों के अनुपात के बराबर होता है।
\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)
गणना:
\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)
⇒ \(64\over81\) = \(({AD\over PT})^2\)
⇒ \(AD\over PT\) = \(\sqrt{64\over81}\) = \(8\over9\)
⇒ \(AD\over 10.8\) = \(8\over9\)
⇒ AD = \({8\times10.8}\over9\) = 9.6 सेमी
∴ AD = 9.6 सेमी
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