The correct option is A 10 cm
Given ABCD is a rhombus.
Hence, AB=BC=CD=DA.
Given, AC=16 cm and BD=12 cm.
Since ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors.
Hence, AE=EC=8 cm and BE=ED=6 cm.
Now, we know that,
∠AEB=∠BEC=∠CED=∠DEA=90°
So, in the triangle AEB, we have
AE=8 cm,BE=6 cm and ∠AEB=90°
By Pythagoreas Theorem,
AE2+BE2=AB2
⇒AB2=82+62=64+36=100
⇒AB2=100
⇒AB=10 cm
Hence, the sides of the rhombus are of length 10 cm.