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In a ΔABC, ∠A = 60°, AB = 3 cm and AC = 4 cm, then find the length of angle bisector AD.
- a)12√5/7 cm
- b)12√7/7 cm
- c)12√11/7 cm
- d)12√3/7 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a ΔABC, ∠A = 60°, AB = 3 cm and AC = 4 cm, then find ...
Area of ΔABC, with ∠A = 60°, AB = 3 cm and AC = 4 cm = 1/2 × AB × AC × sin60
⇒ Area of ΔABC = 1/2 × 3 × 4 × √3/2
Also, area of ΔABD = 1/2 × AB × AD × sin30 = 1/2 × 3 × AD × 1/2 = 1/2 × 3/2 × AD
Similarly, area of ΔADC = 1/2 × AC × AD × sin30 = 1/2 × 4 × AD × 1/2 = 1/2 × 4/2 × AD
⇒ Area of ΔABC = Area of ΔABD + Area of ΔADC
⇒ 1/2 × 3 × 4 × √3/2 = 1/2 × 3/2 × AD + 1/2 × 4/2 × AD
∴ AD = 12√3/7 cm
⇒ Area of ΔABC = 1/2 × 3 × 4 × √3/2
Also, area of ΔABD = 1/2 × AB × AD × sin30 = 1/2 × 3 × AD × 1/2 = 1/2 × 3/2 × AD
Similarly, area of ΔADC = 1/2 × AC × AD × sin30 = 1/2 × 4 × AD × 1/2 = 1/2 × 4/2 × AD
⇒ Area of ΔABC = Area of ΔABD + Area of ΔADC
⇒ 1/2 × 3 × 4 × √3/2 = 1/2 × 3/2 × AD + 1/2 × 4/2 × AD
∴ AD = 12√3/7 cm
Most Upvoted Answer
In a ΔABC, ∠A = 60°, AB = 3 cm and AC = 4 cm, then find ...
Given information:
- ∠A = 60°
- AB = 3 cm
- AC = 4 cm
Calculation:
- Let AD be the angle bisector of ∠A in triangle ABC.
- Using the angle bisector theorem, we can find the length of AD.
Angle Bisector Theorem:
- The angle bisector theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides of the triangle.
Applying Angle Bisector Theorem:
- Let AD = x cm
- According to the angle bisector theorem:
AB/BD = AC/CD
3/x = 4/(3+x)
3(3+x) = 4x
9 + 3x = 4x
x = 9 cm
Therefore, the length of angle bisector AD is:
- AD = 9 cm
Hence, the correct answer is option D) 12√3/7 cm.
- ∠A = 60°
- AB = 3 cm
- AC = 4 cm
Calculation:
- Let AD be the angle bisector of ∠A in triangle ABC.
- Using the angle bisector theorem, we can find the length of AD.
Angle Bisector Theorem:
- The angle bisector theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides of the triangle.
Applying Angle Bisector Theorem:
- Let AD = x cm
- According to the angle bisector theorem:
AB/BD = AC/CD
3/x = 4/(3+x)
3(3+x) = 4x
9 + 3x = 4x
x = 9 cm
Therefore, the length of angle bisector AD is:
- AD = 9 cm
Hence, the correct answer is option D) 12√3/7 cm.
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In a ΔABC, ∠A = 60°, AB = 3 cm and AC = 4 cm, then find ...
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In a ΔABC, ∠A = 60°, AB = 3 cm and AC = 4 cm, then find the length of angle bisector AD.a)12√5/7 cmb)12√7/7 cmc)12√11/7 cmd)12√3/7 cmCorrect answer is option 'D'. Can you explain this answer?
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