ABC एक त्रिभुज है और D भुजा BC पर एक बिंदु है। यदि BC = 16 cm, BD = 11 cm और ∠ADC = ∠BAC है, तो AC की लंबाई बराबर है:

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SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 2)
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  1. 4\(\sqrt5\) cm
  2. 4 cm
  3. 3\(\sqrt5\) cm
  4. 5 cm

Answer (Detailed Solution Below)

Option 1 : 4\(\sqrt5\) cm
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दिया गया है:

BC = 16 cm, BD = 11 cm और ∠ADC = ∠BAC

संकल्पना:

यदि दो त्रिभुजों के दो कोण और एक भुजा बराबर हों, तो दोनों त्रिभुज समरूप होंगे।

गणना:

ΔABC और ΔADC में

⇒ ∠ADC = ∠BAC

⇒ ∠C = दोनों त्रिभुजों में उभयनिष्ठ कोण

⇒ AC = उभयनिष्ठ भुजा

इसलिए, ΔABC और ΔADC समरूप त्रिभुज हैं।

⇒ \({BC\over AC}={AC\over DC}\)

⇒ AC2 = BC × DC

⇒ AC2 = 16 × 5 = 80

⇒ AC = 4√5

∴ अभीष्ट परिणाम 4√5 होगा।

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