The diagonals of a rhombus ABCD intersect at O. If AB = 5 cm, diagonal BD = 8 cm, find the length of other diagonal AC.


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Answer:

6 cm

Step by Step Explanation:
  1. The following figure shows the rhombus ABCD,

    According to the question, AB = 5 cm,
    BD = 8 cm.
  2. We know that the diagonals of a rhombus are perpendicular and bisect each other.
    Therefore, OB =  
    BD
    2
     
    =  
    8
    2
     
    = 4 cm
  3. In right angled ΔAOB,
    OA2 = AB2 - OB2
    ⇒ OA2 = 52 - 42
    ⇒ OA2 = 9
    ⇒ OA2 = 32
    ⇒ OA = 3 cm   [Ignore negative value as OA cannot be negative.]
  4. Hence, the length of the diagonal AC = 2 × OA
    = 2 × 3
    = 6 cm.

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