Math, asked by BrainlyHelper, 1 year ago

The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.

Answers

Answered by nikitasingh79
104

SOLUTION :  

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.

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Answered by VishalSharma01
134

Answer:

Step-by-step explanation:

Given :-

Diagonals of a rhombus are 24 cm and 10 cm.

To Find :-

Side of the rhombus.

Solution :-

Let ABCD be the rhombus.

And AC and BD intersect each other at O.

AO = 1/2 × 10 = 5 cm

BO = 1/2 × 24 = 12 cm

In right angled △AOB,

By applying Pythagoras theorem, we get

AB² = AO² + BO²

⇒ 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.

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