1.

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

Answer»

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.


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