Question
Download Solution PDFअधिकतम आकार के एक वर्ग का क्षेत्रफल ज्ञात कीजिये जो 6 सेमी, 8 सेमी, 10 सेमी की भुजाओं के समकोण त्रिभुज में बना है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
त्रिभुज की भुजा 6 सेमी, 8 सेमी, 10 सेमी हैं।
प्रयुक्त सूत्र:
त्रिभुज का क्षेत्रफल = 1/2 × आधार × ऊँचाई
वर्ग का क्षेत्रफल = भुजा2
गणना:
माना वर्ग की भुजा 'a' है
Δ ABC का क्षेत्रफल = Δ ADE का क्षेत्रफल + Δ EFC का क्षेत्रफल + वर्ग का क्षेत्रफल
⇒ 1/2 × 6 × 8 = 1/2 × a × (8 – a) + 1/2 × (6 – a) × a + a2
⇒ 24 = 7a – a2 + a2
⇒ a = 24/7
वर्ग का क्षेत्रफल = भुजा2 = a2
⇒ (24/7)2
⇒ 576/49
∴ वर्ग का क्षेत्रफल 576/49 सेमी2 हैLast updated on Jun 2, 2025
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