UPSC Exam > UPSC Questions > A polygon has 20 diagonals. How many sides do...
Start Learning for Free
A polygon has 20 diagonals. How many sides does it have?
- a)12
- b)11
- c)10
- d)9
- e)8
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)...
Free Test
FREE
| Start Free Test |
Community Answer
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)...
To determine the number of sides a polygon has given the number of diagonals, we can use a formula that relates the number of sides (n) and the number of diagonals (d). The formula is:
d = n(n-3)/2
where d is the number of diagonals and n is the number of sides.
Let's substitute the given information into the formula:
20 = n(n-3)/2
To solve this equation, we can multiply both sides by 2 to get rid of the fraction:
40 = n(n-3)
Expanding the equation:
40 = n^2 - 3n
Rearranging the equation:
n^2 - 3n - 40 = 0
Factoring the quadratic equation:
(n - 8)(n + 5) = 0
Setting each factor equal to zero:
n - 8 = 0 or n + 5 = 0
Solving for n:
n = 8 or n = -5
Since the number of sides cannot be negative, we discard n = -5 and conclude that the polygon has 8 sides. Therefore, the correct answer is option E) 8.
d = n(n-3)/2
where d is the number of diagonals and n is the number of sides.
Let's substitute the given information into the formula:
20 = n(n-3)/2
To solve this equation, we can multiply both sides by 2 to get rid of the fraction:
40 = n(n-3)
Expanding the equation:
40 = n^2 - 3n
Rearranging the equation:
n^2 - 3n - 40 = 0
Factoring the quadratic equation:
(n - 8)(n + 5) = 0
Setting each factor equal to zero:
n - 8 = 0 or n + 5 = 0
Solving for n:
n = 8 or n = -5
Since the number of sides cannot be negative, we discard n = -5 and conclude that the polygon has 8 sides. Therefore, the correct answer is option E) 8.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer?
Question Description
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer?.
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer?.
Solutions for A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer?, a detailed solution for A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A polygon has 20 diagonals. How many sides does it have?a)12b)11c)10d)9e)8Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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