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30 Apr 2016, 00:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:32) correct
27%
(01:53)
wrong
based on 279
sessions
History
Date
Time
Result
Not Attempted Yet
A polygon has 90 diagonals. How many sides does it have?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Self made
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Self made
30 Apr 2016, 01:41
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The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 90
n*(n - 3) = 180
Substitute n from the answer choices. n = 15
Answer: D
n*(n - 3)/2 = 90
n*(n - 3) = 180
Substitute n from the answer choices. n = 15
Answer: D
General Discussion
30 Apr 2016, 23:52
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To take Vyshak point forward,
the formula for diagonals of an n sided polygon = n*(n - 3)/2 diagonal can be easily derived as follows:
consider a rectangle : 4 sides ABCD
now we know that there are just 2 diagonals here
but to apply the formula, we need to understand it
since there are 4 sides, n=4
but if you take a vertex, say A, it cannot have a diagonal with vertex B or vertex C (the adjacent vertices)
A can form a diagonal only with D
and B can form it with only B
hence when we calculate the no. of diagonals , we multiply sides n with (n-3) {These 3 include the adjacent vertices and point itself}
And we divide the product by 2 to avoid counting the diagonals twice
Here, in this particular problem, when you get the number of diagonals as 90
You can easily use this shortcut : n*(n - 3)/2 = 90
n*(n - 3) = 180 =15 * 12
n=15
Correct Option : D
the formula for diagonals of an n sided polygon = n*(n - 3)/2 diagonal can be easily derived as follows:
consider a rectangle : 4 sides ABCD
now we know that there are just 2 diagonals here
but to apply the formula, we need to understand it
since there are 4 sides, n=4
but if you take a vertex, say A, it cannot have a diagonal with vertex B or vertex C (the adjacent vertices)
A can form a diagonal only with D
and B can form it with only B
hence when we calculate the no. of diagonals , we multiply sides n with (n-3) {These 3 include the adjacent vertices and point itself}
And we divide the product by 2 to avoid counting the diagonals twice
Here, in this particular problem, when you get the number of diagonals as 90
You can easily use this shortcut : n*(n - 3)/2 = 90
n*(n - 3) = 180 =15 * 12
n=15
Correct Option : D
