Question

If the diagonals of a rhombus are 12 cm and 16 cm, then the perimeter of the rhombus is

(A)10 cm (B)40 cm2 (C)40 cm (D)10 cm2

Answer 1

diagonals of a rhombus are perpendicular bisectors of each other
so AO=OC=6cm
and DO=OB=8cm
in triangle AOB
by pythagoras theorm
AB^2=AO^2+OB^2
AB^2=6^2+8^2
AB^2=36+64
AB^2=100
AB=10
but AB is side of rhombus 
so side of rhombus=10cm
perimeter=4 x side
              =4x10
             =40cm
answer is (C) 40 cm
pls refer to the file for figure 

Answer 2

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