CAT Exam > CAT Questions > If the rectangular faces of a brick have thei...
Start Learning for Free
If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is
(2019)
- a)1 : √3
- b)√3 : 2
- c)√2 : √3
- d)2 : √5
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the rectangular faces of a brick have their diagonals in the ratio ...
Let the edges of the brick be a, b, and c such that
a < b < c
a2 + b2 = 32 = 9 ...(i)
a2 + c2 = ( 2√3 )2 = 12 ...(ii)
b2 + c2 = ( √15 )2 = 15 ...(iii)
Adding all three equations. We get
2(a2 + b2 + c2) = 9 + 12 + 15 = 36
a2 + b2 + c2 = 18 ...(iv)
From (i) and (iv), c2 = 18 – 9 ⇒ c = 3
From (iii) and (iv) a2 = 18 – 15 ⇒ a = 3
Therefore, required ratio =
a < b < c
a2 + b2 = 32 = 9 ...(i)
a2 + c2 = ( 2√3 )2 = 12 ...(ii)
b2 + c2 = ( √15 )2 = 15 ...(iii)
Adding all three equations. We get
2(a2 + b2 + c2) = 9 + 12 + 15 = 36
a2 + b2 + c2 = 18 ...(iv)
From (i) and (iv), c2 = 18 – 9 ⇒ c = 3
From (iii) and (iv) a2 = 18 – 15 ⇒ a = 3
Therefore, required ratio =
Most Upvoted Answer
If the rectangular faces of a brick have their diagonals in the ratio ...
Let the length, width, and height of the brick be l, w, and h, respectively.
According to the given condition, the diagonals of the rectangular faces have a ratio of 3:2.
The diagonal of a rectangular face can be found using the Pythagorean theorem. For the first face, the diagonal is √(l^2 + w^2).
For the second face, the diagonal is √(l^2 + h^2).
For the third face, the diagonal is √(w^2 + h^2).
Since the diagonals are in a ratio of 3:2, we can write the following equations:
√(l^2 + w^2) : √(l^2 + h^2) = 3 : 2 ...(1)
√(l^2 + h^2) : √(w^2 + h^2) = 3 : 2 ...(2)
Squaring both sides of equation (1), we get:
(l^2 + w^2) : (l^2 + h^2) = 9 : 4
Cross-multiplying, we have:
4(l^2 + w^2) = 9(l^2 + h^2)
4l^2 + 4w^2 = 9l^2 + 9h^2
5l^2 - 4h^2 = 4w^2 ...(3)
Similarly, squaring both sides of equation (2), we get:
(l^2 + h^2) : (w^2 + h^2) = 9 : 4
Cross-multiplying, we have:
4(l^2 + h^2) = 9(w^2 + h^2)
4l^2 + 4h^2 = 9w^2 + 9h^2
4l^2 - 9w^2 = 5h^2 ...(4)
From equations (3) and (4), we have the system of equations:
5l^2 - 4h^2 = 4w^2 ...(5)
4l^2 - 9w^2 = 5h^2 ...(6)
To find a specific solution, we need additional information or constraints.
According to the given condition, the diagonals of the rectangular faces have a ratio of 3:2.
The diagonal of a rectangular face can be found using the Pythagorean theorem. For the first face, the diagonal is √(l^2 + w^2).
For the second face, the diagonal is √(l^2 + h^2).
For the third face, the diagonal is √(w^2 + h^2).
Since the diagonals are in a ratio of 3:2, we can write the following equations:
√(l^2 + w^2) : √(l^2 + h^2) = 3 : 2 ...(1)
√(l^2 + h^2) : √(w^2 + h^2) = 3 : 2 ...(2)
Squaring both sides of equation (1), we get:
(l^2 + w^2) : (l^2 + h^2) = 9 : 4
Cross-multiplying, we have:
4(l^2 + w^2) = 9(l^2 + h^2)
4l^2 + 4w^2 = 9l^2 + 9h^2
5l^2 - 4h^2 = 4w^2 ...(3)
Similarly, squaring both sides of equation (2), we get:
(l^2 + h^2) : (w^2 + h^2) = 9 : 4
Cross-multiplying, we have:
4(l^2 + h^2) = 9(w^2 + h^2)
4l^2 + 4h^2 = 9w^2 + 9h^2
4l^2 - 9w^2 = 5h^2 ...(4)
From equations (3) and (4), we have the system of equations:
5l^2 - 4h^2 = 4w^2 ...(5)
4l^2 - 9w^2 = 5h^2 ...(6)
To find a specific solution, we need additional information or constraints.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer?
Question Description
If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct 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 the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct 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 the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer?.
If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct 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 the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct 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 the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the rectangular faces of a brick have their diagonals in the ratio 3 : 2√3 : √15 , then the ratio of the length of the shortest edge of the brick to that of its longest edge is(2019)a)1 : √3b)√3 : 2c)√2 : √3d)2 : √5Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup