JEE Exam > JEE Questions > If in an equilateral triangle, inradius is a ...
Start Learning for Free
If in an equilateral triangle, inradius is a rational number then which of the following is not true.
- a)circumradius is always rational
- b)Exradii are always rational
- c)Area is always irrational
- d)Perimeter is always rational
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If in an equilateral triangle, inradius is a rational number then whic...
Most Upvoted Answer
If in an equilateral triangle, inradius is a rational number then whic...
Free Test
FREE
| Start Free Test |
Community Answer
If in an equilateral triangle, inradius is a rational number then whic...
Explanation:
Given: In an equilateral triangle, the inradius is a rational number.
Circumradius:
- The circumradius of an equilateral triangle can be calculated using the formula R = 2r, where R is the circumradius and r is the inradius.
- Since the inradius is given to be rational, the circumradius will also be rational (as it is twice the inradius).
- Therefore, the statement that the circumradius is always rational is true.
Exradii:
- Exradii are the radii of the three excircles of the triangle.
- The exradii are related to the inradius by the formula r1 = r2 = r3 = r, where r1, r2, r3 are the exradii and r is the inradius.
- Since the inradius is rational, the exradii will also be rational.
- Therefore, the statement that the exradii are always rational is true.
Area:
- The area of an equilateral triangle can be calculated using the formula A = (s^2 * √3) / 4, where A is the area and s is the side length of the triangle.
- Since the side length of an equilateral triangle is directly related to the inradius (s = 3r), and the inradius is rational, the side length will also be rational.
- However, the area formula involves the square root of 3, which is an irrational number.
- Therefore, the statement that the area is always irrational is true.
Perimeter:
- The perimeter of an equilateral triangle is simply 3 times the side length, which, as mentioned earlier, is rational.
- Therefore, the perimeter of the equilateral triangle will always be rational.
- The statement that the perimeter is always rational is not true.
Therefore, the correct answer is option 'D', as the perimeter of the equilateral triangle is not always rational when the inradius is a rational number.
Given: In an equilateral triangle, the inradius is a rational number.
Circumradius:
- The circumradius of an equilateral triangle can be calculated using the formula R = 2r, where R is the circumradius and r is the inradius.
- Since the inradius is given to be rational, the circumradius will also be rational (as it is twice the inradius).
- Therefore, the statement that the circumradius is always rational is true.
Exradii:
- Exradii are the radii of the three excircles of the triangle.
- The exradii are related to the inradius by the formula r1 = r2 = r3 = r, where r1, r2, r3 are the exradii and r is the inradius.
- Since the inradius is rational, the exradii will also be rational.
- Therefore, the statement that the exradii are always rational is true.
Area:
- The area of an equilateral triangle can be calculated using the formula A = (s^2 * √3) / 4, where A is the area and s is the side length of the triangle.
- Since the side length of an equilateral triangle is directly related to the inradius (s = 3r), and the inradius is rational, the side length will also be rational.
- However, the area formula involves the square root of 3, which is an irrational number.
- Therefore, the statement that the area is always irrational is true.
Perimeter:
- The perimeter of an equilateral triangle is simply 3 times the side length, which, as mentioned earlier, is rational.
- Therefore, the perimeter of the equilateral triangle will always be rational.
- The statement that the perimeter is always rational is not true.
Therefore, the correct answer is option 'D', as the perimeter of the equilateral triangle is not always rational when the inradius is a rational number.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer?
Question Description
If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer?.
If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer?.
Solutions for If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If in an equilateral triangle, inradius is a rational number then which of the following is not true.a)circumradius is always rationalb)Exradii are always rationalc)Area is always irrationald)Perimeter is always rationalCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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