Q. 34.1( 26 Votes )

# The perimeter of

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 :

BO^{2} = AB^{2} – AO^{2}

⇒BO^{2} = AB^{2} – AO^{2}

⇒BO^{2} = 45^{2} – 36^{2}

⇒BO^{2} = 2025 – 1296

⇒BO^{2} = 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 cm^{2}

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