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If the diagonals of a rhombus are 24 and 10, then the value of thrice its side is
- a)39
- b)36
- c)33
- d)42
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the diagonals of a rhombus are 24 and 10, then the value of thrice ...
Half of each of the two diagonal forms the two sides of a right - angled triangle whose hypotenuse is the side of the rhombus.
Length of Diagonal 1 = 24
Length of Diagonal 2 = 10
⇒ Sides of the triangle = 12 and 5
Length of Diagonal 1 = 24
Length of Diagonal 2 = 10
⇒ Sides of the triangle = 12 and 5
Since it’s a right - angled triangle, it should follow Pythagoras theorem.
⇒ (Side)2 = (12)2 + (5)2
⇒ Side = 13
∴ Side of the rhombus = 13.
⇒ Thrice the value of the side = 3 × 13 = 39
⇒ (Side)2 = (12)2 + (5)2
⇒ Side = 13
∴ Side of the rhombus = 13.
⇒ Thrice the value of the side = 3 × 13 = 39
Most Upvoted Answer
If the diagonals of a rhombus are 24 and 10, then the value of thrice ...
Given: Diagonals of a rhombus = 24 and 10
To find: Thrice the side of the rhombus
Formula: In a rhombus, diagonals are perpendicular bisectors of each other and bisect the angles into two equal parts.
Therefore, let's draw a rhombus and label the diagonals as AB and CD, where AB = 24 and CD = 10.
Let's draw the perpendicular bisectors of AB and CD and mark the intersection as E.
Let's mark the side of the rhombus as x. As per the formula, AE = BE = AB/2 = 24/2 = 12 and CE = DE = CD/2 = 10/2 = 5.
Now, let's apply the Pythagoras theorem in triangles AEC and BED to find the value of x.
In triangle AEC, AC^2 = AE^2 + EC^2
=> AC^2 = 12^2 + x^2
In triangle BED, BD^2 = BE^2 + ED^2
=> BD^2 = 12^2 + x^2
As per the formula, AC = BD = diagonal of a rhombus
=> 24^2 + x^2 = 10^2 + x^2
=> 576 = 100
This is not possible. Hence, the given values of the diagonals cannot form a rhombus.
Therefore, the answer to the question is "Data inadequate" or "Not possible to form a rhombus with given diagonal lengths."
To find: Thrice the side of the rhombus
Formula: In a rhombus, diagonals are perpendicular bisectors of each other and bisect the angles into two equal parts.
Therefore, let's draw a rhombus and label the diagonals as AB and CD, where AB = 24 and CD = 10.
Let's draw the perpendicular bisectors of AB and CD and mark the intersection as E.
Let's mark the side of the rhombus as x. As per the formula, AE = BE = AB/2 = 24/2 = 12 and CE = DE = CD/2 = 10/2 = 5.
Now, let's apply the Pythagoras theorem in triangles AEC and BED to find the value of x.
In triangle AEC, AC^2 = AE^2 + EC^2
=> AC^2 = 12^2 + x^2
In triangle BED, BD^2 = BE^2 + ED^2
=> BD^2 = 12^2 + x^2
As per the formula, AC = BD = diagonal of a rhombus
=> 24^2 + x^2 = 10^2 + x^2
=> 576 = 100
This is not possible. Hence, the given values of the diagonals cannot form a rhombus.
Therefore, the answer to the question is "Data inadequate" or "Not possible to form a rhombus with given diagonal lengths."
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If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer?
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If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer?.
If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the diagonals of a rhombus are 24 and 10, then the value of thrice its side isa)39b)36c)33d)42Correct answer is option 'A'. Can you explain this answer?.
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