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Question
How many different (mutually noncongruent) trapeziums can be constructed using four distinct side lengths from the set {1,3,4,5,6}?
How many different (mutually noncongruent) trapeziums can be constructed using four distinct side lengths from the set {1,3,4,5,6}?
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Solution
The correct option is B 11
Using property,
|a−c|<(b+d)<(a+c)
Possible cases:
(b,d)(a,c)(1,3)(5,6)(1,3)(4,5)(1,3)(4,6)(1,4)(5,6)(1,4)(3,6)(1,4)(3,5)(1,5)(4,6)(1,5)(3,6)(1,5)(3,4)(1,6)(4,5)(1,6)(3,5)
Hence total number of possible cases is 11.
Using property,
|a−c|<(b+d)<(a+c)
Possible cases:
(b,d)(a,c)(1,3)(5,6)(1,3)(4,5)(1,3)(4,6)(1,4)(5,6)(1,4)(3,6)(1,4)(3,5)(1,5)(4,6)(1,5)(3,6)(1,5)(3,4)(1,6)(4,5)(1,6)(3,5)
Hence total number of possible cases is 11.
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