If one diagonal of a rhombus of side 13 cm is 10 cm, then

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AC = 10 cm. AO = OC = 5 cm.
∠ AOB = 90° AB = 13 cm.
From ∆AOB,
∴ OB = √AB² - OA²
= √13² + 5² = √169 - 25
= √144 = 12 cm.
∴ BD = 2OB = 2 × 12 = 24 cm.