# The perimeter of

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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