Class 9 Exam > Class 9 Questions > Given the product of diagonals of a rhombus A...
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Given the product of diagonals of a rhombus ABCD is 2500 cm2, its area is
- a)1250 cm2
- b)625 cm2
- c)1200 cm2
- d)2000 cm2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Given the product of diagonals of a rhombus ABCD is 2500cm2, its area ...
Area of rhombus = 1/2 * (Product of diagonal of rhombus)
= 2500/2 = 1250 cm2.
= 2500/2 = 1250 cm2.
Most Upvoted Answer
Given the product of diagonals of a rhombus ABCD is 2500cm2, its area ...
Explanation:
Therefore, the area of the rhombus is 1250cm^2, which is option A.
- A rhombus is a quadrilateral in which all sides are equal.
- Diagonals of a rhombus bisect each other.
- Let AC and BD be the diagonals of the rhombus ABCD.
- Since diagonals of a rhombus bisect each other, let the length of each diagonal be 2x.
- Therefore, AC = 2x and BD = 2x.
- Product of diagonals = AC x BD = 2x x 2x = 4x^2.
- Given, product of diagonals = 2500cm^2.
- 4x^2 = 2500cm^2
- x^2 = 625cm^2
- x = 25cm (since x represents the length of half of a diagonal and it can't be negative)
- Area of rhombus = (AC x BD)/2
- Area of rhombus = (2x x 2x)/2 = 2x^2
- Substituting x = 25cm, we get area of rhombus = 2x^2 = 2(25)^2 = 1250cm^2
Therefore, the area of the rhombus is 1250cm^2, which is option A.
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Given the product of diagonals of a rhombus ABCD is 2500cm2, its area ...
Option A is correct...
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