Question

If the diagonals of a rhombus measure 18 cm and 24 cm, its side will be :​

Answer 1

Step-by-step explanation:

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

We know that diagonals of the rhombus bisect eachother 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 ∆AOB is a right angled triangle.

By Pythagoras Theorem, we get,

$ab ^{2} = ao ^{2} + bo ^{2} \\ ab = \sqrt{ao ^{2} } + bo ^{2} \\ ab = \sqrt{9 ^{2} } + 12 ^{2} \\ ab = \sqrt{225 } \\ ab = 15cm$

so its side will be 15cm