Question 464282
As we know the diagonals of the rhombus are perpendicular bisectors. To find the side of the rhombus we use the Pythagorean theorem :

{{{x^2=12^2+5^2=144+25=169}}} <=> {{{x=sqrt(169)}}} <=> {{{x=13 cm}}}.

Since the sides of the rhombus are equal its perimeter is:{{{4*13cm=52cm}}}.