Question

The lengths of the diagonals of a rhombus are 6 cm and 8 cm. What will be length of each side of rhombus ​

Answer 1

Answer:

We know diagonals bisects at right angle

∴ In △AOD

AO^2 + OD^2=AD^2

3^2 + 4^2 =AD^2

⇒AD=5cm

Step-by-step explanation:

Please refer to the above image to clarify your doubt

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Answer 2

Given:

The length of the diagonals of the rhombus is

• Diagonal 1 = 6cm
• Diagonal 2 = 8cm

To find:

The length of each side of the rhombus

Look at the attached image,

The rhombus is named ABCD, where AC and BD are the diagonals 8cm and 6 cm respectively.

Some properties of the rhombus,

• The diagonals bisect each other and are perpendicular to each other.
• All four sides of the rhombus are equal.

Now,

AO = CO = 1/2 AC = 8/2 = 4 cm

OD = OB = 1/2 BD = 6/2 = 3 cm

And,

AB = BC = CD = AD

We get four right-angled triangles ΔAOB, ΔBOC, ΔCOD, ΔDOA

We may take any triangle,

• Taking ΔAOB, right-angled at ∠AOB

By using Pythagoras Theorem,

(AO)² + (OB)² = (AB)²

⇒ (4)² + (3)² = (AB)²

⇒ 16 + 9 = (AB)²

⇒ 25 = (AB)²

⇒ √25 = AB

⇒ 5 = AB

Thus,

The one side of the rhombus is 5 cm

Now,

As, AB = BC = CD = AD

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