Question

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

Options

• 16 cm

• 15 cm

• 20 cm

• 17 cm

Answer 1

Let ABCD be rhombus with diagonals AC and BD 18cm and 24cm respectively.

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

Therefore,

`AO = 1/2 AC `

`AO = 1/2 (18cm) `

AO = 9cm

Similarly,

`BO = 1/2 BD `

`BO = 1/2(24cm)`

BO = 12cm

Also, ΔAOB is a right angled triangle.

By Pythagoras theorem, we get:

`AB^2 = AO^2 + BO^2`

    `AB = sqrt(AO^2 + BO^2)`

    `AB = sqrt(9^2 + 12^2)`

    `AB = sqrt225`

     AB = 15cm

Hence the correct choice is (b).