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No of sides in a quadrilateral
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Updated on: 29 Jun 2021, 15:42
Updated on: 29 Jun 2021, 15:42
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20% (03:02) correct
79% (02:17) wrong based on 24 sessions
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Given that the length of each side of a quadrilateral is a distinct integer and that the longest side is not greater than 7, how many different possible combinations of side lengths are there?
A. 21
B. 24
C. 32
D. 34
E. 35
A. 21
B. 24
C. 32
D. 34
E. 35
Re: No of sides in a quadrilateral
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17 Mar 2019, 01:31
17 Mar 2019, 01:31
Expert Reply
Since the length of each side of a quadrilateral is a distinct integer and that the longest side is not greater than 7, all four sides must be taken from the set {1, 2, 3, 4, 5, 6, 7}. How many different sets of four could be selected? \(7C4\)= 7*6*5/(3!) = 7*5 = 35 Of those 35, the only ones that don’t work for sides of a quadrilateral are the ones in which the sum of the three smallest sides are equal to or less than the longest side. These would be
1 + 2 + 3 < 7
1 + 2 + 3 = 6
1 + 2 + 4 = 7
Those are the only invalid combinations. The other 32 work.
Answer = (C)
1 + 2 + 3 < 7
1 + 2 + 3 = 6
1 + 2 + 4 = 7
Those are the only invalid combinations. The other 32 work.
Answer = (C)
Re: No of sides in a quadrilateral
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10 Mar 2024, 04:40
10 Mar 2024, 04:40
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