Q. 235.0( 1 Vote )

# If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to

A. 16 cm

B. 15 cm

C. 20 cm

D. 17 cm

Answer :

ABCD is a rhombus

AC = 18cm

BD = 24cm

We have to find the sides of the rhombus

In triangle AOB,

AO = 9cm (Diagonals of a parallelogram bisect each other)

BO = 12cm

AOB is a right - triangle right angled at O (Diagonals of a rhombus are perpendicular to each other)

So,

AB^{2} = AO^{2} + BO^{2} (By Pythagoras theorem)

AB^{2} = 9^{2} + 12^{2}

AB^{2} = 81 + 144

AB^{2} = 225

AB = 15cm

In a rhombus, all sides are equal

Thus, each side of the rhombus is 15cm.

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