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A convex polygon has 14 diagonals. How many sides does the polygon have?
- a)5
- b)6
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A convex polygon has 14 diagonals. How many sides does the polygon hav...
No. of diagonals in a polygon of n sides = n (n – 3 ) / 2
14 = n (n – 3) / 2
14 × 2 = n ( n – 3)
28 = n ( n – 3)
28 = 7 (7 -3)
Therefore n = 7
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Community Answer
A convex polygon has 14 diagonals. How many sides does the polygon hav...
Explanation:
To solve this problem, we need to understand the concept of diagonals in a convex polygon.
Diagonals in a Convex Polygon:
A diagonal is a line segment that connects two non-adjacent vertices of a polygon. In a convex polygon with n sides, the number of diagonals can be calculated using the formula:
Number of diagonals = (n * (n-3))/2
Solving the Problem:
Given that the polygon has 14 diagonals, we can set up the equation:
14 = (n * (n-3))/2
Multiplying both sides of the equation by 2, we get:
28 = n * (n-3)
Expanding the equation, we have:
28 = n^2 - 3n
Rearranging the equation, we have:
n^2 - 3n - 28 = 0
Now, we need to factorize the quadratic equation to find the values of n.
The factors of -28 that add up to -3 are -7 and 4.
Therefore, the equation can be factored as:
(n - 7)(n + 4) = 0
Setting each factor equal to zero, we get:
n - 7 = 0 or n + 4 = 0
Solving for n, we have:
n = 7 or n = -4
Since the number of sides of a polygon cannot be negative, we can discard the solution n = -4.
Therefore, the polygon has 7 sides.
Hence, the correct answer is option C.
To solve this problem, we need to understand the concept of diagonals in a convex polygon.
Diagonals in a Convex Polygon:
A diagonal is a line segment that connects two non-adjacent vertices of a polygon. In a convex polygon with n sides, the number of diagonals can be calculated using the formula:
Number of diagonals = (n * (n-3))/2
Solving the Problem:
Given that the polygon has 14 diagonals, we can set up the equation:
14 = (n * (n-3))/2
Multiplying both sides of the equation by 2, we get:
28 = n * (n-3)
Expanding the equation, we have:
28 = n^2 - 3n
Rearranging the equation, we have:
n^2 - 3n - 28 = 0
Now, we need to factorize the quadratic equation to find the values of n.
The factors of -28 that add up to -3 are -7 and 4.
Therefore, the equation can be factored as:
(n - 7)(n + 4) = 0
Setting each factor equal to zero, we get:
n - 7 = 0 or n + 4 = 0
Solving for n, we have:
n = 7 or n = -4
Since the number of sides of a polygon cannot be negative, we can discard the solution n = -4.
Therefore, the polygon has 7 sides.
Hence, the correct answer is option C.
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A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?
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A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?.
A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex polygon has 14 diagonals. How many sides does the polygon have?a)5b)6c)7d)8Correct answer is option 'C'. Can you explain this answer?.
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