Question

How to find the perimeter of a rhombus if the diagonals are given?

Answer 1

consider a rhombus ABCD ,
let AC be x and BD be y for

now the point where the diagonals join can be named O
since diagonals of a rhombus bisect one another ,
AO=CO= x/2 and DO=BO=y/2

Consider triangle AOB ,
AB squared = AO squared + BO squared ( By pythagors theory )
AB = x squared /4 + y squared/ 4

4AB = perimeter ( since all the sides of a rhombus are equal )

4 x ( x squared + y squared ) / 4 = perimeter

perimeter ==> x squared + y squared
perimeter ==> sum of squares of diagonals