Question

Find the length of each side of a rhombus whose diagonals are 40cm and 30cm.

Answer 1

We know the diagonals of a rhombus bisect each other at right angles.

30/2 = 15 
40/2 = 20

let each side be x

therefore

x^2 = 15^2 + 20^2
x^2= 225 + 400
x^2=625
x = 25

Hope this will help you ...

Answer 2

$\huge\sf\pink{Answer}$

☞ Length of the sides = 25 cm

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$\huge\sf\blue{Given}$

✭ Diagonals of a rhombus are 30 cm and 40 cm

$\rule{110}1$

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

☆ All sides?

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$\huge\sf\purple{Steps}$

Let AC = 30 cm and BD = 40 cm

We know that,

The diagonals of a rhombus bisect each other at right angles

Therefore,

➳ AO = OC = 15 cm

➳ BO = OD = 20 cm

Now In ΔBOC,

➢ BO = 15 cm

➢ OC = 20 cm

➢ ${\sf\angle BOC = 90\degree}$

Using Pythagoras theorem,

➝ BC² = BO² + OC²

➝ BC² = (15)² + (20)²

➝ BC² = 225 + 400

➝ BC² = 625

➝ BC = √625

➝ $\sf\color{lime}{BC = 25 \ cm}$

$\rule{170}3$