Question

13. If the diagonals of a rhombus are 12 cm and 16 cm, find the length of each side.​

Answer 1

Answer:

$\large{\underline{\boxed{\sf Each \: side = 10 \: cm}}}$

Step-by-step explanation:

Given that ;

Diagonals of a rhombus are 12 cm and 16 cm.

Let AC = 12 cm and BD = 16 cm

We know that,

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

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

⇒ BC = 10 cm

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

Hence, the length of each side of rhombus is 10 cm.

Answer 2

Answer : 10 cm.

Solution :-

We know that half the length of the diagonal and a side of a rhombus forms a right angled triangle.

Thus,

» 1/2 × 12 cm = 6 cm 

» 1/2 × 16 cm = 8 cm

Let the side of the rhombus be x cm.

Then,

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10 cm

Hence, the side of the rhombus is 10 cm.