The length of side of a rhombus is 17 cm and one of its diagonals is 1

1.	The length of side of a rhombus is 17 cm and one of its diagonals is 16 cm. Find the area of rhombus.1. 120 cm22. 240 cm23. 360 cm24. 480 cm2
Answer» Correct Answer - Option 2 : 240 cm2 Given: Length of side = 17 cm Length of a diagonal = 16 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 Calculations: Let AC = 16 cm and BD = x cm If the two diagonals of rhombus ABCD intersect at O then, ⇒ AO² + BO² = AB² ⇒ (16/2)² + (x/2)² = 17² ⇒ 64 + (x²/4) = 289 ⇒ (x²/4) = 225 ⇒ x² = 900 ⇒ x = 30 cm Area of rhombus = (1/2) × 16 × 30 ⇒ 8 × 30 ⇒ 240 cm² ∴ The area of the rhombus is 240 cm²

The length of side of a rhombus is 17 cm and one of its diagonals is 16 cm. Find the area of rhombus.1. 120 cm22. 240 cm23. 360 cm24. 480 cm2

Answer» Correct Answer - Option 2 : 240 cm2

Given:

Length of side = 17 cm

Length of a diagonal = 16 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

Calculations:

Let AC = 16 cm and BD = x cm

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

⇒ AO² + BO² = AB²

⇒ (16/2)² + (x/2)² = 17²

⇒ 64 + (x²/4) = 289

⇒ (x²/4) = 225

⇒ x² = 900

⇒ x = 30 cm

Area of rhombus = (1/2) × 16 × 30

⇒ 8 × 30

⇒ 240 cm²

∴ The area of the rhombus is 240 cm²

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