Question

the diagonals of a rhombus are 6cm and 8cm. find the length of each side of the rhombus​

Answer 1

Answer:

here is your answer. ...

Answer 2

Answer:

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

Given :-

The diagonals of a rhombus are 8cm and 6cm.

To find :-

Find the length of each side of the rhombus.

Hence ,

Let ABCD be the rhombus whose diagonals AC and BD are the lengths 6 cm and 8 cm respectively.

Since,

The diagonals of a rhombus are perpendicular bisects of each other .

Therefore,

$OA \: = \frac{1}{2} \times BD = \frac{1}{2} \times 8cm \: = 4cm$

Now,

In right - angled △AOB

$AB ^{2} = OA ^{2} = OB ^{2} </p><p>$

(By Pythogoras theorem)

$= > AB^{2} = 9 + 16$

$= > AB ^{2} = 25 = > AB = 5cm$

Therefore,

The length of each side of the rhombus is 5 cm .

$= > AB ^{2} = (3) ^{2} + (4) ^{2}$