Question

if diagonals of a rhombus are 10 CM , 24 CM, find the length of side ​

Answer 1

GIVEN : Diagonals of a rhombus are 24 cm & 10 cm.

Let ABCD be a rhombus with diagonals AC = 10 cm and BD = 24 cm.

We know that diagonal of a rhombus bisect each other at 90°. AO = OC & OB = OD & ∠AOB = ∠AOD = ∠BOC = ∠COD = 90°.

Therefore, AO = OC = 5 cm and BO = OD = 12 cm.

In ∆AOB,

AB² = OA² + OB²

[By using Pythagoras theorem]

AB² = 5² + 12²

AB² = 25 + 144

AB²  = 169

AB =  √169  

AB = 13 cm.

Hence, the length of the each side of the rhombus is 13 cm.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

Let ABCD be the rhombus where, AC=10cm and BD=24cm

Let AC and BD intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

Thus, we have

AO=

2

1

×AC=

2

1

×10=5cm and

BO=

2

1

×BD=

2

1

×24=12cm

In right angled △AOB,

⇒ (AB)

2

=(AO)

2

+(BO)

2

⇒ (AB)

2

=(5)

2

+(12)

2

⇒ (AB)

2

=25+144

⇒ (AB)

2

=169

∴ AB=13cm

∴ The length of each side of rhombus is 13cm.