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A polygon has 44 diagonals then the number of its sides are:
- a)8
- b)9
- c)10
- d)11
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10...
Solution:
To find the number of sides of a polygon that has 44 diagonals, we can use the formula:
Number of diagonals of an n-sided polygon = n(n-3)/2
where n is the number of sides.
We are given that the number of diagonals in the polygon is 44. So, we can set up the equation:
44 = n(n-3)/2
Multiplying both sides by 2 gives:
88 = n(n-3)
Expanding the right-hand side gives:
88 = n^2 - 3n
Rearranging gives:
n^2 - 3n - 88 = 0
We can now solve for n using the quadratic formula:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = -88.
Plugging in these values gives:
n = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
n = (3 ± sqrt(361)) / 2
n = (3 ± 19) / 2
We take the positive root since the number of sides of a polygon cannot be negative. So:
n = (3 + 19) / 2
n = 11
Therefore, the polygon has 11 sides.
To find the number of sides of a polygon that has 44 diagonals, we can use the formula:
Number of diagonals of an n-sided polygon = n(n-3)/2
where n is the number of sides.
We are given that the number of diagonals in the polygon is 44. So, we can set up the equation:
44 = n(n-3)/2
Multiplying both sides by 2 gives:
88 = n(n-3)
Expanding the right-hand side gives:
88 = n^2 - 3n
Rearranging gives:
n^2 - 3n - 88 = 0
We can now solve for n using the quadratic formula:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = -88.
Plugging in these values gives:
n = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
n = (3 ± sqrt(361)) / 2
n = (3 ± 19) / 2
We take the positive root since the number of sides of a polygon cannot be negative. So:
n = (3 + 19) / 2
n = 11
Therefore, the polygon has 11 sides.
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Community Answer
A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10...
Total no of lines from n points is nC2 and total sides of polygon = n
(combination of two points out of n )- ( no of sides i.e n)= no of diagonal
nC2 - n = 44
n(n-1)/2-n=44
n(n-1)/2= 44+n
n^2-n= 88+2n
n^2-3n-88=0
n^2-11n+8n-88=0
n(n-11)+8(n-11)
(n+8) (n-11)
n=-8 and n=11
so we'll take n= 11
(combination of two points out of n )- ( no of sides i.e n)= no of diagonal
nC2 - n = 44
n(n-1)/2-n=44
n(n-1)/2= 44+n
n^2-n= 88+2n
n^2-3n-88=0
n^2-11n+8n-88=0
n(n-11)+8(n-11)
(n+8) (n-11)
n=-8 and n=11
so we'll take n= 11
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A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10d)11Correct answer is option 'D'. Can you explain this answer?
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A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10d)11Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10d)11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 44 diagonals then the number of its sides are:a)8b)9c)10d)11Correct answer is option 'D'. Can you explain this answer?.
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