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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Step by Step Explanation:
- The following figure shows the rhombus ABCD,
According to the question, AB = 5 cm,
BD = 8 cm.
- We know that the diagonals of a rhombus are perpendicular and bisect each other.
Therefore, OB =
= 4 cm
- 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.]
- Hence, the length of the diagonal AC = 2 × OA
= 2 × 3
= 6 cm.