Q. 235.0( 1 Vote )

# If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal toA. 16 cmB. 15 cmC. 20 cmD. 17 cm

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,

AB2 = AO2 + BO2 (By Pythagoras theorem)

AB2 = 92 + 122

AB2 = 81 + 144

AB2 = 225

AB = 15cm

In a rhombus, all sides are equal

Thus, each side of the rhombus is 15cm.

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