The perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm

1.	The perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm then find the area of the rhombus.1. 384 cm22. 240 cm23. 340 cm24. 278 cm2
Answer» Correct Answer - Option 2 : 240 cm² Given: Perimeter of rhombus = 68 cm Diagonal, (d1) = 30 cm Formula used: Perimeter = 4 × side Area of Rhombus = (d1 × d2)/2 Area of Rhombus = Side × Altitude d12 + d22 = 4 × s2 Here, d1, d2, and s are diagonals and side of rhombus respectively. Concept used: All sides of a rhombus are equal and diagonals bisect each other at a right angle. Calculation: Perimeter = 4 × side ⇒ 68 = 4 × side ⇒ side = 17 cm Now, d12 + d22 = 4 × s2 ⇒ 302 + d22 = 4 × 172 ⇒ d22 = 256 ⇒ d2 = 16 Now, Area of Rhombus = (d1 × d2)/2 ⇒ Area of Rhombus = (30 × 16)/2 ∴ Area of Rhombus is 240 cm2

The perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm then find the area of the rhombus.1. 384 cm22. 240 cm23. 340 cm24. 278 cm2

Answer» Correct Answer - Option 2 : 240 cm²

Given:

Perimeter of rhombus = 68 cm

Diagonal, (d1) = 30 cm

Formula used:

Perimeter = 4 × side

Area of Rhombus = (d1 × d2)/2

Area of Rhombus = Side × Altitude

d12 + d22 = 4 × s2

Here, d1, d2, and s are diagonals and side of rhombus respectively.

Concept used:

All sides of a rhombus are equal and diagonals bisect each other at a right angle.

Calculation:

Perimeter = 4 × side

⇒ 68 = 4 × side

⇒ side = 17 cm

Now, d12 + d22 = 4 × s2

⇒ 302 + d22 = 4 × 172

⇒ d22 = 256

⇒ d2 = 16

Now, Area of Rhombus = (d1 × d2)/2

⇒ Area of Rhombus = (30 × 16)/2

∴ Area of Rhombus is 240 cm2

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