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If the rectangular faces of a brick have their diagonals in the ratio 
then the ratio of the length of the shortest edge of the brick to that of its longest edge is
then the ratio of the length of the shortest edge of the brick to that of its longest edge is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the rectangular faces of a brick have their diagonals in the ratio ...
Assuming the dimensions of the brick are a, b and c and the diagonals are 3, 2
√3 and √15
Hence, a2 + b2 = 32 ...(1)
b2 + c2 = (2√3)2 ...(2)
c2 + a2 = (√15)2 ...(3)
Adding the three equations,
2(a2 + b2 + c2) = 9 + 12 + 15 = 36
⇒ a2 + b2 + c2 = 18....(4)
Subtracting (1) from (4), we get c2= 9 ⇒ c = 3
Subtracting (2) from (4), we get = 6 ⇒ a = √6
Subtracting (3) from (4), we get = 3 ⇒ b = √3
The ratio of the length of the shortest edge of the brick to that of its longest edge is =
√3 / 3 = 1 : √3
√3 and √15
Hence, a2 + b2 = 32 ...(1)
b2 + c2 = (2√3)2 ...(2)
c2 + a2 = (√15)2 ...(3)
Adding the three equations,
2(a2 + b2 + c2) = 9 + 12 + 15 = 36
⇒ a2 + b2 + c2 = 18....(4)
Subtracting (1) from (4), we get c2= 9 ⇒ c = 3
Subtracting (2) from (4), we get = 6 ⇒ a = √6
Subtracting (3) from (4), we get = 3 ⇒ b = √3
The ratio of the length of the shortest edge of the brick to that of its longest edge is =
√3 / 3 = 1 : √3
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If the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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If the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. 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 the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. 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 the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
If the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. 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 the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. 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 the rectangular faces of a brick have their diagonals in the ratio then the ratio of the length of the shortest edge of the brick to that of its longest edge isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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