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diagonals of a rhombus are perpendicular bisectors of each other
so AO=OC=6cm
and DO=OB=8cm
in triangle AOB
by pythagoras theorm
but AB is side of rhombus 
so side of rhombus=10cm
perimeter=4 x side
answer is (C) 40 cm
pls refer to the file for figure 
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Let ABCD be the rhombus. And the diagonals AC=12cm and BD= 16 cm
Let the diagonals intersects at O.
We know the diagonals of rhombus are perpendicular to each other and bisect each other.
Hence triangle BOC is a right angle triangle with
                       side OB =12/2 = 6 cm and side OC =16/2 = 8cm
Hence we have BC= √(6²+8²)= 10 cm
Perimeter of Rhombus= 4*10 = 40 cm
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