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Mathematics

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :

  1. 3 cm

  2. 5 cm

  3. 7 cm

  4. 9 cm

Pythagoras Theorem

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Answer

Let AC = 6 cm and BD = 8 cm.

The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is : Pythagoras Theorem, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

We know that,

Diagonals of rhombus are perpendicular and bisect each other,

OB = 12\dfrac{1}{2} BD = 4 cm and AO = 12\dfrac{1}{2} AC = 3 cm.

In right triangle AOB,

By pythagoras theorem we get,

Hypotenuse2 = Base2 + Height2

⇒ AB2 = AO2 + OB2

⇒ AB2 = 32 + 42

⇒ AB2 = 9 + 16

⇒ AB2 = 25

⇒ AB = 25\sqrt{25} = 5 cm.

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

Hence, option 2 is the correct option.

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