Question

The lengths of the diagonals of a rhombus are 8 cm and 6 cm. Its each side is​

Answer 1

Answer:

its each side is 5 cm by application of Pythagoras theorem

Answer 2

✬ Each Side = 5 cm ✬

Step-by-step explanation:

Given:

• Length of diagonals of rhombus are 8 and 6 cm.

To Find:

• What is the measure of each side of rhombus?

Solution: Let ABCD be a rhombus in which:-

• Diagonal AC = 8 cm
• Diagonal BD = 6 cm

➟ As we know that diagonals of rhombus bisect each other perpendicularly i.e at 90°.

∴ OA = OC = 1/2 x AC

➙ OA = OC = 1/2 x 8 = 4 cm.

∴ OB = OD = 1/2 x BD

➙ OB = OD = 1/2 x 6 = 3 cm.

• In ∆AOB •

• OA = 4 cm ( Perpendicular )
• OB = 3 cm ( Base )
• ∠AOB = 90°
• AB = ? ( Hypotenuse )

Applying Pythagoras Theorem in ∆AOB

★ Pythagoras Theorem = Base² + Perpendicular² = Hypotenuse² ★

$\implies{\rm }$ OB² + OA² = AB²

$\implies{\rm }$ 3² + 4² = AB²

$\implies{\rm }$ 9 + 16 = AB²

$\implies{\rm }$ 25 = AB²

$\implies{\rm }$ √5 x 5 = AB

$\implies{\rm }$ 5 cm = AB

Since, the all four sides of rhombus are equal to each other therefore measure of each side will be 5 cm.