The area of a rhombus is 216 cm2 and one of the diagonals is 18 cm. Fi

1.	The area of a rhombus is 216 cm2 and one of the diagonals is 18 cm. Find the perimeter of the rhombus.1. 15 cm2. 24 cm3. 60 cm4. 48 cm
Answer» Correct Answer - Option 3 : 60 cm Given: Area of the rhombus is 216 cm² Length of a diagonal = 18 cm Concept used: The two diagonals bisect each other at 90° in a rhombus. Formula used: Area of rhombus = (1/2) × Product of the two diagonals Perimeter = 4 × (Side of the rhombus) Calculations: Let the second diagonal of the rhombus be x and the side of the rhombus be a Area of rhombus = (1/2) × 18 × x ⇒ 216 = (1/2) × 18x ⇒ 18x = 432 ⇒ x = 24 cm If the two diagonals of rhombus ABCD intersect at O then, ⇒ AO² + BO² = AB² ⇒ (18/2)² + (24/2)² = a² ⇒ 81 + 144 = a² ⇒ a² = 225 ⇒ a = 15 cm Perimeter of the rhombus = 4a ⇒ 4 × 15 ⇒ 60 cm ∴ The perimeter of the rhombus is 60 cm.

The area of a rhombus is 216 cm2 and one of the diagonals is 18 cm. Find the perimeter of the rhombus.1. 15 cm2. 24 cm3. 60 cm4. 48 cm

Answer» Correct Answer - Option 3 : 60 cm

Given:

Area of the rhombus is 216 cm²

Length of a diagonal = 18 cm

Concept used:

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

Formula used:

Area of rhombus = (1/2) × Product of the two diagonals

Perimeter = 4 × (Side of the rhombus)

Calculations:

Let the second diagonal of the rhombus be x and the side of the rhombus be a

Area of rhombus = (1/2) × 18 × x

⇒ 216 = (1/2) × 18x

⇒ 18x = 432

⇒ x = 24 cm

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

⇒ AO² + BO² = AB²

⇒ (18/2)² + (24/2)² = a²

⇒ 81 + 144 = a²

⇒ a² = 225

⇒ a = 15 cm

Perimeter of the rhombus = 4a

⇒ 4 × 15

⇒ 60 cm

∴ The perimeter of the rhombus is 60 cm.

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