Quant Exam > Quant Questions > The ratio of the area of a square to that of ...
Start Learning for Free
The ratio of the area of a square to that of the square drawn on the its the diagonal is
- a)1:4
- b)2:1
- c)1:2
- d)1:3
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The ratio of the area of a square to that of the square drawn on the i...
Most Upvoted Answer
The ratio of the area of a square to that of the square drawn on the i...
The ratio of the area of a square to that of the square drawn on its diagonal can be determined by understanding the relationship between the sides of a square and its diagonal.
Understanding the relationship between the sides and diagonal of a square:
- In a square, all sides are equal in length.
- The diagonal of a square is a line segment that connects two opposite vertices.
- The diagonal of a square divides it into two congruent right triangles.
Explaining the solution:
To find the ratio of the areas, we can assume the length of one side of the square as 's'.
- The area of the square is given by A = s^2.
- The length of the diagonal of the square can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of the right triangle.
- The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- In this case, the hypotenuse is the diagonal, and the other two sides are the sides of the square.
- Applying the Pythagorean theorem, we have d^2 = s^2 + s^2 = 2s^2.
- Taking the square root of both sides, we get d = sqrt(2s^2) = sqrt(2)s.
Calculating the ratio of the areas:
- The area of the square drawn on the diagonal is given by A_d = (sqrt(2)s)^2 = 2s^2.
- Dividing the area of the square by the area of the square drawn on the diagonal, we get A/A_d = s^2 / 2s^2 = 1/2.
Therefore, the ratio of the area of the square to that of the square drawn on its diagonal is 1:2, which corresponds to option 'C'.
Understanding the relationship between the sides and diagonal of a square:
- In a square, all sides are equal in length.
- The diagonal of a square is a line segment that connects two opposite vertices.
- The diagonal of a square divides it into two congruent right triangles.
Explaining the solution:
To find the ratio of the areas, we can assume the length of one side of the square as 's'.
- The area of the square is given by A = s^2.
- The length of the diagonal of the square can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of the right triangle.
- The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- In this case, the hypotenuse is the diagonal, and the other two sides are the sides of the square.
- Applying the Pythagorean theorem, we have d^2 = s^2 + s^2 = 2s^2.
- Taking the square root of both sides, we get d = sqrt(2s^2) = sqrt(2)s.
Calculating the ratio of the areas:
- The area of the square drawn on the diagonal is given by A_d = (sqrt(2)s)^2 = 2s^2.
- Dividing the area of the square by the area of the square drawn on the diagonal, we get A/A_d = s^2 / 2s^2 = 1/2.
Therefore, the ratio of the area of the square to that of the square drawn on its diagonal is 1:2, which corresponds to option 'C'.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer?
Question Description
The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer?.
The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer?.
Solutions for The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The ratio of the area of a square to that of the square drawn on the its the diagonal isa)1:4b)2:1c)1:2d)1:3Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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