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So the diagonals of the rhombus are at 90°

so the height of the rhombus is 8 cm and base is 15 cm 

so using Pythagoras  we get the length  of 1 side is  \sqrt{8^2+15^2} = 17 cm 

so perimeter is 4 x 17 = 68 cm 
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The diagonals of the rhombus are perpendicular to each other and bisects each other
So the sides of the rhombus is = √{(16/2)² + (30/2)²}
                                             = 17 cm 

Hence perimeter is  17*4 = 68 cm