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In rhombus ABCD, ∠DAB = 60° and each side is 8 cm. How long is the longer diagonal AC?

Class 9Rectangle, Rhombus and SquareGeometry — Quadrilaterals
  • A8 cm
  • B8√3 cm
  • C4√3 cm
  • D16 cm

Step-by-Step Solution

BD = 8 cm (△ABD is equilateral), so OB = 4. In right △AOB: AO = √(64 − 16) = √48 = 4√3, hence AC = 8√3 cm. (4√3 is only half.)
Answer: B) 8√3 cm

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