Question

The length of diagonal of a rhombus are 30 and 40cm then length side is what?

Answer 1

Answer:

$\large{\underline{\boxed{\sf Each \: side = 25 \: cm}}}$

Step-by-step explanation:

Given that ;

Diagonals of a rhombus are 30 cm and 40 cm.

Let AC = 30 cm and BD = 40 cm

We know that,

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

Therefore,

AO = OC = 15 cm

BO = OD = 20 cm

Now, In ΔBOC,

BO = 15 cm

OC = 20 cm

∠BOC = 90°

Using Pythagoras theorem,

BC² = BO² + OC²

⇒ BC² = (15)² + (20)²

⇒ BC² = 225 + 400

⇒ BC² = 625

⇒ BC = √625

⇒ BC = 25 cm

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

Hence, the length of each side of rhombus is 25 cm.

Answer 2

Answer : 25 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 × 30 cm = 15 cm 

» 1/2 × 40 cm = 20 cm

Let the side of the rhombus be x cm.

Then,

x² = 15² + 20²

x² = 225 + 400

x² = 625

x = √625

x = 25 cm

Hence, the side of the rhombus is 25 cm.