Question

the length of the diagonals of a rhombus are 24 cm and 18cm respectively find the length of the each of the Rhombus

Answer 1

Your question needs a correction.

Correct question  : find the length of the each side of the rhombus.

     Solution :-

We know that the diagonals of rhombus bisects each other at 90°.

    By Pythagoras Theorem,

⇒ ( 1 / 2 x 1st Diagonal )^2 + ( 1 / 2 x 2nd diagonal )^2 = side^2

⇒ ( 1 / 2 x 24 cm )^2 + ( 1 / 2 x 18 cm ) = side^2

⇒ ( 12 cm )^2 + ( 9 cm )^2 = side^2

⇒ 144 cm^2 + 81 cm^2 = side^2

⇒ 255 cm^2 = side^2

⇒ ( 15 cm )^2 = side^2

⇒ 15 cm = side

Therefore the length of each side of the rhombus is 15 cm.

Answer 2

Here is your solution

Given :-

The length of the diagonals  of rhombus are 24 cm and 18 cm.

To find length  of rhombus:-

We know that

The diagonals of rhombus bisects each other at 90°.

Now using  Pythagoras Theorem:-

=>(1/2 x 1st Diagonal)^2 + (1/2x2nd diagonal )^2 = side^2

=>( 1/2 x 24 cm )^2 + ( 1 /  x 18 cm ) = side^2

=>( 12 cm )^2 + ( 9 cm )^2 = side^2

=>144 cm^2 + 81 cm^2 = side^2

=>255 cm^2 = side^2

=>( 15 cm )^2 = side^2

=>15 cm = side

Hence

The length of each side of the rhombus is 15 cm.

Hope it helps you