Question

If the diagonals of a rhombus are 9 cm an12 cm find its S​

Answer 1

Step-by-step explanation:

Answer:

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

Eachside=7.5cm

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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.

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: CoRreCt QuEsTiOn :- \: \star}}}}}$

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

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

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

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

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,

$AO \: = \: OC \: = \: 4.5 cm \\ </p><p>BO \: = \: OD \: = \: 6 cm \\ </p><p>Now , \: In \: ΔBOC, \\ </p><p>BO \: = \: 8 cm \\ </p><p>OC \: = \: 6 cm \\ </p><p>∠BOC \: = \: 90°$

Using Pythagoras theorem,

$BC² \: = \: BO² \: + \: OC² \\ </p><p>⇒ \: BC² \: = \: (4.5)² \: + \: 6² \\ </p><p>⇒ \: BC² \: = \: 20.25 \: + \: 36 \\ </p><p>⇒ \: BC² \: = \: 56.25 \\ </p><p>⇒ \: BC \: = \: √56.25 \\ </p><p>⇒ \: BC \: = \: 7.5 cm$

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

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

The length of each side of rhombus is 7.5 cm.