Answer :


Given: A rhombus


Diagonal AC = 72 cm


Perimeter = 180 cm


Perimeter of the rhombus = 4x


Therefore 4x = 180


x= 45


hence, the side length of the rhombus is 45 cm


We know that diagonals of the rhombus bisect each other right angles.


AO = AC


AO = ( × 72) cm


AO = 36 cm


From right AOB, we have :


BO2 = AB2 – AO2


BO2 = AB2 – AO2


BO2 = 452 – 362


BO2 = 2025 – 1296


BO2 = 729


BO = 27 cm


BD = 2× BO


BD = 2 × 27 = 54 cm


Hence, the length of the other diagonal is 54 cm.


Area of the rhombus = × 72 × 54 = 1944 cm2


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