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In a triangle ABC, the lengths of the side AB, AC and BC are 3 ,5 and 6 cm respectively. If a point D on BC drawn such that the line AD bisects the angle A internally ,then what is the length of BD?
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In a triangle ABC, the lengths of the side AB, AC and BC are 3 ,5 and ...
Given:

  • Side AB = 3 cm

  • Side AC = 5 cm

  • Side BC = 6 cm

  • AD bisects angle A internally



To find: Length of BD

Solution:

  • Use the Angle Bisector Theorem: In a triangle ABC, if a line BD bisects angle A, then AB/BD = AC/DC. Using this theorem, we can find the value of DC.

  • Let the length of BD be x. Using the angle bisector theorem, we can write:


    • AB/BD = AC/DC

    • 3/x = 5/(6-x)

    • 18 - 3x = 5x

    • 8x = 18

    • x = 2.25 cm


  • Therefore, the length of BD is 2.25 cm.

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In a triangle ABC, the lengths of the side AB, AC and BC are 3 ,5 and 6 cm respectively. If a point D on BC drawn such that the line AD bisects the angle A internally ,then what is the length of BD?
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