ABC একটি ত্রিভুজ এবং D হল BC বাহুর একটি বিন্দু। যদি BC = 16 সেমি, BD = 11 সেমি এবং ∠ADC = ∠BAC হয়, তাহলে AC এর দৈর্ঘ্য সমান:

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

Answer (Detailed Solution Below)

Option 1 : 4 \(\sqrt5\) সেমি
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Detailed Solution

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প্রদত্ত:

BC = 16 সেমি, BD = 11 সেমি এবং ∠ADC = ∠BAC

ধারণা:

যদি দুটি কোণ এবং দুটি ত্রিভুজের একটি বাহু সমান হয়, তাহলে উভয় ত্রিভুজ AA বৈশিষ্ট্য দ্বারা অনুরূপ হবে।

গণনা:

ΔABC এবং ΔDAC-তে

⇒ ∠ADC = ∠BAC

⇒ ∠C = উভয় ত্রিভুজের সাধারণ কোণ

অতএব, ΔABC এবং ΔDAC অনুরূপ ত্রিভুজ।

\({BC\over AC}={AC\over DC}\)

⇒ AC2 = BC × DC

⇒ AC2 = 16 × 5 = 80

⇒ AC = 4√5

∴  নির্ণেয় ফলাফল হবে 4√5

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