Question
Download Solution PDFमाना, Δ ABC ~ Δ QPR है और \(\rm \frac{area \ of \ \Delta ABC}{area \ of \ \Delta PQR}=\frac{64}{25}\) है। यदि QP = 12 सेमी, PR = 10 सेमी और AC = 15 सेमी है, तो AB की लंबाई ज्ञात कीजिए:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
Δ ABC ~ Δ QPR
\(\frac{area \ of \ Δ ABC}{area \ of \ Δ PQR}=\frac{64}{25}\)
प्रयुक्त सूत्र:
समान त्रिभुजों में, क्षेत्रफलों का अनुपात संगत भुजाओं के अनुपात के वर्ग के बराबर होता है।
\(\frac{area \ of \ Δ ABC}{area \ of \ Δ PQR} = (\frac{corresponding \ side \ of \ Δ ABC}{corresponding \ side \ of \ Δ PQR})^2\)
गणना:
\(\frac{64}{25} = (\frac{AB}{QP})^2\)
⇒ \(\frac{64}{25} = (\frac{AB}{12})^2\)
⇒ \(\frac{64}{25} = \frac{AB^2}{144}\)
⇒ \(\frac{64}{25} × 144 = AB^2\)
⇒ \(\frac{64 × 144}{25} = AB^2\)
⇒ \(\frac{9216}{25} = AB^2\)
⇒ 368.64 = \(AB^2\)
⇒ AB = \(\sqrt{368.64}\)
⇒ AB = 19.2 सेमी
∴ सही उत्तर विकल्प (4) है।
Last updated on Apr 24, 2025
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