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In a ΔABC, AB = 12 cm, ∠ABC = 30°, ∠ACD = 45°and AD is perpendicular on BC, find the area of ΔABC.
  • a)
    18(√3 + 1) cm2
  • b)
    6(√3 + 1) cm2
  • c)
    12(√3 + 1) cm2
  • d)
    18(√3 + 3) cm2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a ΔABC, AB = 12 cm, ∠ABC = 30°, ∠ACD = 45°and...

In ΔABD, sin30° = AD/12
⇒ AD = 6 cm
cos30° = BD/12
⇒ BD = 6√3 cm
In ΔACD, tan45° = AD/CD
⇒ CD = 6 cm
⇒ BC = 6√3 + 6 = 6(√3 + 1) cm
⇒ Area = 1/2 × 6(√3 + 1) × 6
∴ Area = 18(√3 + 1) cm2
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Most Upvoted Answer
In a ΔABC, AB = 12 cm, ∠ABC = 30°, ∠ACD = 45°and...

In ΔABD, sin30° = AD/12
⇒ AD = 6 cm
cos30° = BD/12
⇒ BD = 6√3 cm
In ΔACD, tan45° = AD/CD
⇒ CD = 6 cm
⇒ BC = 6√3 + 6 = 6(√3 + 1) cm
⇒ Area = 1/2 × 6(√3 + 1) × 6
∴ Area = 18(√3 + 1) cm2
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In a ΔABC, AB = 12 cm, ∠ABC = 30°, ∠ACD = 45°and AD is perpendicular on BC, find the area of ΔABC.a)18(√3 + 1) cm2b)6(√3 + 1) cm2c)12(√3 + 1) cm2d)18(√3 + 3) cm2Correct answer is option 'A'. Can you explain this answer?
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