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If th e side o f a rhom bus is 13 c m and the length its one diagonal is 24 c m . Find the area of the rhombus.
- a)120 cm2
- b)105 cm2
- c)142 cm2
- d)144 cm2
- e)110 cm2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If th e side o f a rhom bus is 13 c m and the length its one diagonal...
Given
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Side of rhombus = 13 cm
Length of one diagonal = 24 cm
We know that,
Area of rhombus = 
Length of other diagonal= 
=10 cm
Area of rhombus =
Hence, the correct option is (A).
Most Upvoted Answer
If th e side o f a rhom bus is 13 c m and the length its one diagonal...
Given
Side of rhombus = 13 cm
Length of one diagonal = 24 cm
We know that,
Area of rhombus = 
Length of other diagonal= 
=10 cm
Area of rhombus =
Hence, the correct option is (A).
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Community Answer
If th e side o f a rhom bus is 13 c m and the length its one diagonal...
Understanding the Rhombus
A rhombus is a type of quadrilateral where all sides have equal length and opposite angles are equal. The area can be calculated using the lengths of its diagonals or the base and height.
Given Data
- Side length of the rhombus (s) = 13 cm
- Length of one diagonal (d1) = 24 cm
Finding the Other Diagonal
To find the area, we first need both diagonals. The diagonals of a rhombus bisect each other at right angles. Let the other diagonal be d2.
Using the Pythagorean theorem in one of the triangles formed by the diagonals:
- Half of diagonal 1 = d1/2 = 12 cm
- Half of diagonal 2 = d2/2
- The relationship becomes:
s^2 = (d1/2)^2 + (d2/2)^2
Plugging in the values:
13^2 = 12^2 + (d2/2)^2
This simplifies to:
169 = 144 + (d2/2)^2
Solving for (d2/2)^2 gives:
(d2/2)^2 = 25
d2/2 = 5
Thus, d2 = 10 cm.
Calculating the Area
Now that we have both diagonals:
- d1 = 24 cm
- d2 = 10 cm
The formula for the area (A) of a rhombus is:
A = (d1 * d2) / 2
Substituting the values:
A = (24 * 10) / 2 = 240 / 2 = 120 cm²
Conclusion
The area of the rhombus is 120 cm², confirming that the correct answer is option 'A'.
A rhombus is a type of quadrilateral where all sides have equal length and opposite angles are equal. The area can be calculated using the lengths of its diagonals or the base and height.
Given Data
- Side length of the rhombus (s) = 13 cm
- Length of one diagonal (d1) = 24 cm
Finding the Other Diagonal
To find the area, we first need both diagonals. The diagonals of a rhombus bisect each other at right angles. Let the other diagonal be d2.
Using the Pythagorean theorem in one of the triangles formed by the diagonals:
- Half of diagonal 1 = d1/2 = 12 cm
- Half of diagonal 2 = d2/2
- The relationship becomes:
s^2 = (d1/2)^2 + (d2/2)^2
Plugging in the values:
13^2 = 12^2 + (d2/2)^2
This simplifies to:
169 = 144 + (d2/2)^2
Solving for (d2/2)^2 gives:
(d2/2)^2 = 25
d2/2 = 5
Thus, d2 = 10 cm.
Calculating the Area
Now that we have both diagonals:
- d1 = 24 cm
- d2 = 10 cm
The formula for the area (A) of a rhombus is:
A = (d1 * d2) / 2
Substituting the values:
A = (24 * 10) / 2 = 240 / 2 = 120 cm²
Conclusion
The area of the rhombus is 120 cm², confirming that the correct answer is option 'A'.
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If th e side o f a rhom bus is 13 c m and the length its one diagonal is 24 c m . Find the area of the rhombus.a)120 cm2b)105 cm2c)142 cm2d)144 cm2e)110 cm2Correct answer is option 'A'. Can you explain this answer?
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If th e side o f a rhom bus is 13 c m and the length its one diagonal is 24 c m . Find the area of the rhombus.a)120 cm2b)105 cm2c)142 cm2d)144 cm2e)110 cm2Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If th e side o f a rhom bus is 13 c m and the length its one diagonal is 24 c m . Find the area of the rhombus.a)120 cm2b)105 cm2c)142 cm2d)144 cm2e)110 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If th e side o f a rhom bus is 13 c m and the length its one diagonal is 24 c m . Find the area of the rhombus.a)120 cm2b)105 cm2c)142 cm2d)144 cm2e)110 cm2Correct answer is option 'A'. Can you explain this answer?.
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