त्रिभुज ABC में, AD कोण A का कोण समद्विभाजक है। यदि AB = 8.4 सेमी और AC = 5.6 सेमी और DC = 2.8 सेमी है, तो भुजा BC की लम्बाई कितनी होगी?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)
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  1. 4.2 सेमी
  2. 5.6 सेमी
  3. 7 सेमी
  4. 2.8 सेमी

Answer (Detailed Solution Below)

Option 3 : 7 सेमी
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दिया गया है:

AB = 8.4 सेमी, और AC = 5.6 सेमी, DC = 2.8 सेमी

प्रयुक्त अवधारणा:

त्रिभुज का कोण समद्विभाजक सम्मुख भुजा को त्रिभुज की अन्य दो भुजाओं के समानुपाती दो भागों में विभाजित करता है।

गणना:

 

अवधारणा के अनुसार,

AB/AC = BD/DC

⇒ 8.4/5.6 = BD/2.8

⇒ 8.4/2 = BD

⇒ 4.2 = BD

इसलिए, BD + DC = BC

BC = 4.2 + 2.8

⇒ 7 सेमी

∴ भुजा BC की लम्बाई 7 सेमी होगी।

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