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A polygon has 54 diagonals, then the number of its sides arc :
- a)11
- b)12
- c)7
- d)none
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A polygon has 54 diagonals, then the number of its sides arc :a)11b)12...
We have a very good formula
where x in number of diagonal and n stand for number of sides so putting the value.
where x in number of diagonal and n stand for number of sides so putting the value.
Most Upvoted Answer
A polygon has 54 diagonals, then the number of its sides arc :a)11b)12...
To determine the number of sides in a polygon given the number of diagonals, we can use a mathematical formula.
Understanding the Formula for Diagonals
The formula to calculate the number of diagonals (D) in a polygon with 'n' sides is:
D = n(n - 3) / 2
Where:
- D = number of diagonals
- n = number of sides
Given Information
In this case, we know that D = 54. Therefore, we can set up the equation:
54 = n(n - 3) / 2
Solving the Equation
To eliminate the fraction, multiply both sides by 2:
108 = n(n - 3)
Now, expand and rearrange the equation:
n² - 3n - 108 = 0
This is a quadratic equation in standard form.
Applying the Quadratic Formula
We can solve this equation using the quadratic formula, which is:
n = [ -b ± √(b² - 4ac) ] / 2a
Here, a = 1, b = -3, and c = -108. Plugging in these values:
n = [ 3 ± √((-3)² - 4 * 1 * (-108)) ] / 2 * 1
Calculate the discriminant:
= [ 3 ± √(9 + 432) ] / 2
= [ 3 ± √441 ] / 2
= [ 3 ± 21 ] / 2
Finding the Values of n
Calculating the two possible values:
1. n = (3 + 21) / 2 = 12
2. n = (3 - 21) / 2 = -9 (not valid since sides cannot be negative)
Thus, the number of sides in the polygon is:
n = 12
Hence, the correct answer is option 'B'.
Understanding the Formula for Diagonals
The formula to calculate the number of diagonals (D) in a polygon with 'n' sides is:
D = n(n - 3) / 2
Where:
- D = number of diagonals
- n = number of sides
Given Information
In this case, we know that D = 54. Therefore, we can set up the equation:
54 = n(n - 3) / 2
Solving the Equation
To eliminate the fraction, multiply both sides by 2:
108 = n(n - 3)
Now, expand and rearrange the equation:
n² - 3n - 108 = 0
This is a quadratic equation in standard form.
Applying the Quadratic Formula
We can solve this equation using the quadratic formula, which is:
n = [ -b ± √(b² - 4ac) ] / 2a
Here, a = 1, b = -3, and c = -108. Plugging in these values:
n = [ 3 ± √((-3)² - 4 * 1 * (-108)) ] / 2 * 1
Calculate the discriminant:
= [ 3 ± √(9 + 432) ] / 2
= [ 3 ± √441 ] / 2
= [ 3 ± 21 ] / 2
Finding the Values of n
Calculating the two possible values:
1. n = (3 + 21) / 2 = 12
2. n = (3 - 21) / 2 = -9 (not valid since sides cannot be negative)
Thus, the number of sides in the polygon is:
n = 12
Hence, the correct answer is option 'B'.
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Community Answer
A polygon has 54 diagonals, then the number of its sides arc :a)11b)12...
We have a very good formula
where x in number of diagonal and n stand for number of sides so putting the value.
where x in number of diagonal and n stand for number of sides so putting the value.
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A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer?
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A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer?.
A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polygon has 54 diagonals, then the number of its sides arc :a)11b)12c)7d)noneCorrect answer is option 'B'. Can you explain this answer?.
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