JEE Exam > JEE Questions > A polygon has 44 diagonals. The number of its...
Start Learning for Free
A polygon has 44 diagonals. The number of its sides is
- a)10
- b)11
- c)12
- d)13
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13...
Solution:
Given, the polygon has 44 diagonals.
Let the number of sides of the polygon be n.
Formula:
The number of diagonals in a polygon with n sides = n(n-3)/2
Substitute the given value of diagonals in the formula,
44 = n(n-3)/2
88 = n(n-3)
n^2 - 3n - 88 = 0
Factorizing the above quadratic equation, we get
(n-11)(n+8) = 0
n = 11 or n = -8
Since n represents the number of sides of a polygon, we can eliminate the negative value of n.
Therefore, the number of sides of the polygon is 11.
Hence, option B is the correct answer.
Note:
The formula used above is derived by considering any vertex of the polygon and counting the number of diagonals that can be drawn from that vertex. We can observe that the number of diagonals drawn from a vertex is equal to the number of vertices excluding the adjacent vertices. Hence, adding up the number of diagonals from all the vertices and dividing by 2 gives the total number of diagonals in the polygon.
Given, the polygon has 44 diagonals.
Let the number of sides of the polygon be n.
Formula:
The number of diagonals in a polygon with n sides = n(n-3)/2
Substitute the given value of diagonals in the formula,
44 = n(n-3)/2
88 = n(n-3)
n^2 - 3n - 88 = 0
Factorizing the above quadratic equation, we get
(n-11)(n+8) = 0
n = 11 or n = -8
Since n represents the number of sides of a polygon, we can eliminate the negative value of n.
Therefore, the number of sides of the polygon is 11.
Hence, option B is the correct answer.
Note:
The formula used above is derived by considering any vertex of the polygon and counting the number of diagonals that can be drawn from that vertex. We can observe that the number of diagonals drawn from a vertex is equal to the number of vertices excluding the adjacent vertices. Hence, adding up the number of diagonals from all the vertices and dividing by 2 gives the total number of diagonals in the polygon.
Free Test
FREE
| Start Free Test |
Community Answer
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13...
The number of diagonals for n sided polygon = [n(n-3)]/2 .therefore,=> 44 = [n(n-3)]/2 .=> n^2 - 3n - 88 = 0 .=> (n+8)(n-11) =0.=> n = -8 or 11.Neglect n = -8.Therefore,=> n = 11 .therefore, the no. of sides = 11Hence, correct answer is (B).
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?
Question Description
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?.
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?.
Solutions for A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. 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 A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A polygon has 44 diagonals. The number of its sides isa)10b)11c)12d)13Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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