Question

. The diagonals of rhombus are 12 cm and 16 cm. Find the length of each side of rhombus.

Answer 1

Answer:

10cm

Step-by-step explanation:

In a rhombus diagonals divide equally when they are bisected each other at 90°

So, AC=12

AO+OC=12

2AO=12

AO=6=OC

lly, BD=16

OB=OD=8cm

ACCORDING TO DIAGRAM,

Tri(AOB) IS RIGHT ANGLED AT O

AB*2=OA*2+OB*2

AB*2=8*2+6*2

AB*2=64+36

AB*2=100

AB=10

AS RHOMBUS HAVE EQUAL SIDES

SO, AB=BC=CD=AD=10cm

Answer 2

$\huge\sf\pink{Answer}$

☞ Length of sides = 10 cm

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Diagonals of a rhombus are 12 cm and 16 cm

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ Length of the sides?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let AC = 12 cm and BD = 16 cm

We know that,

The diagonals of a rhombus bisect each other at right angles,

Therefore,

◕ AO = OC = 6 cm

◕ BO = OD = 8 cm

Now, In ΔBOC,

➢ BO = 8 cm

➢ OC = 6 cm

➢ ∠BOC = 90°

Using Pythagoras theorem,

➝ BC² = BO² + OC²

➝ BC² = 8² + 6²

➝ BC² = 64 + 36

➝ BC² = 100

➝ BC = √100

➝$\sf\color{aqua}{ BC = 10 \ cm}$

$\rule{170}3$