Question

If the diagonals of a rhombus are 9 cm and 12 cm find its sides

Answer 1

area of rohmus = d₁.d₂ × 1/2

(9×12)÷2

108÷2

54 cm²

thanks..

Answer 2

Answer:

$\large{\underline{\boxed{\sf Each \: side = 7.5 \: cm}}}$

Step-by-step explanation:

Given that ;

Diagonals of a rhombus are 9 cm and 12 cm.

Let AC = 9 cm and BD = 12 cm

We know that,

The diagonals of a rhombus bisect each other at right angles, i.e., 90°

Therefore,

AO = OC = 4.5 cm

BO = OD = 6 cm

Now, In ΔBOC,

BO = 8 cm

OC = 6 cm

∠BOC = 90°

Using Pythagoras theorem,

BC² = BO² + OC²

⇒ BC² = (4.5)² + 6²

⇒ BC² = 20.25 + 36

⇒ BC² = 56.25

⇒ BC = √56.25

⇒ BC = 7.5 cm

Also, we know that each side of rhombus is equal.

Hence, the length of each side of rhombus is 7.5 cm.