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The perimeter of a rhombus is 100 cm and the length of its smaller diagonal is 14 cm. Find the area of the rhombus?
- a)236 cm2
- b)356 cm2
- c)306 cm2
- d)336 cm2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The perimeter of a rhombus is 100 cm and the length of its smaller dia...
Perimeter of Rhombus = 4 × Side
⇒ 100 cm = 4 × side
⇒ Each Side of Rhombus = 100/4 = 25 cm
In triangle AOB;
(AB)2 = (OB)2 + (AO)2
⇒ (25)2 = (7)2 + (AO)2
⇒ (AO)2 = 625 - 49
⇒ (AO)2 = 576 cm2
⇒ AO = 24 cm
The value of AC = 2 × AO
The value of AC = 2 × 24 = 48 cm
Area of Rhombus ABCD = (1/2) × 48 × 14 = 336 cm2
∴ The area of rhombus ABCD is 336 cm2
⇒ 100 cm = 4 × side
⇒ Each Side of Rhombus = 100/4 = 25 cm
In triangle AOB;
(AB)2 = (OB)2 + (AO)2
⇒ (25)2 = (7)2 + (AO)2
⇒ (AO)2 = 625 - 49
⇒ (AO)2 = 576 cm2
⇒ AO = 24 cm
The value of AC = 2 × AO
The value of AC = 2 × 24 = 48 cm
Area of Rhombus ABCD = (1/2) × 48 × 14 = 336 cm2
∴ The area of rhombus ABCD is 336 cm2
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The perimeter of a rhombus is 100 cm and the length of its smaller diagonal is 14 cm. Find the area of the rhombus?a)236 cm2b)356 cm2c)306 cm2d)336 cm2Correct answer is option 'D'. Can you explain this answer?
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