यदि दो समरूप त्रिभुजों की संगत भुजाओं का अनुपात √3 ∶ √2 है, तो दोनों त्रिभुजों के क्षेत्रफल का अनुपात क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 3)
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  1. 3 ∶ 2
  2. 9 ∶ 4
  3. √3 ∶ √2
  4. 27 ∶ 8

Answer (Detailed Solution Below)

Option 1 : 3 ∶ 2
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दिया गया है:

दो समरूप त्रिभुजों की संगत भुजाओं का अनुपात = √3 : √2

प्रयुक्त सूत्र:

पहले त्रिभुज का क्षेत्रफल/दूसरे त्रिभुज का क्षेत्रफल = (पहले त्रिभुज की भुजा/दूसरे त्रिभुज की संगत भुजाएँ)2

गणना:

पहले त्रिभुज का क्षेत्रफल/दूसरे त्रिभुज का क्षेत्रफल = (√3/√2)2 = 3/2

∴ दो समरूप त्रिभुजों के क्षेत्रफल का अनुपात 3 ∶ 2 है।

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