The perimeter of a rhombus is 100 cm and one of the two diagonals is 1

1.	The perimeter of a rhombus is 100 cm and one of the two diagonals is 14 cm. Find the difference between the two diagonals.1. 48 cm2. 25 cm3. 62 cm4. 34 cm
Answer» Correct Answer - Option 4 : 34 cm Given: Perimeter of a rhombus is 100 cm Length of diagonal = 14 cm Concept used: The two diagonals bisect each other at 90° in a rhombus. Formula used: Perimeter = 4 × (Side of the rhombus) Calculations: Let the side of rhombus be x and the diagonals be a and b Perimeter = 4x ⇒ 100 = 4x ⇒ x = 25 cm If the two diagonals of rhombus ABCD intersect at O then, ⇒ AO² + BO² = AB² ⇒ (14/2)² + (b/2)² = 25² ⇒ 49 + (b²/4) = 625 ⇒ (b²/4) = 576 ⇒ b² = 2304 ⇒ b = 48 cm Difference between the diagonals = b – a ⇒ 48 – 14 ⇒ 34 cm ∴ The difference between the two diagonals is 34 cm

The perimeter of a rhombus is 100 cm and one of the two diagonals is 14 cm. Find the difference between the two diagonals.1. 48 cm2. 25 cm3. 62 cm4. 34 cm

Answer» Correct Answer - Option 4 : 34 cm

Given:

Perimeter of a rhombus is 100 cm

Length of diagonal = 14 cm

Concept used:

The two diagonals bisect each other at 90° in a rhombus.

Formula used:

Perimeter = 4 × (Side of the rhombus)

Calculations:

Let the side of rhombus be x and the diagonals be a and b

Perimeter = 4x

⇒ 100 = 4x

⇒ x = 25 cm

If the two diagonals of rhombus ABCD intersect at O then,

⇒ AO² + BO² = AB²

⇒ (14/2)² + (b/2)² = 25²

⇒ 49 + (b²/4) = 625

⇒ (b²/4) = 576

⇒ b² = 2304

⇒ b = 48 cm

Difference between the diagonals = b – a

⇒ 48 – 14

⇒ 34 cm

∴ The difference between the two diagonals is 34 cm

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