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Question

The number of noncongruent integer-sided triangles whose sides belong to the set {10,11,12,...,22} is

A
283
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B
446
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C
448
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D
449
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Solution

The correct option is C 283
For the scalene triangle , select any three sides from the set which can be done in 13C3=286 ways
But sum of two sides is greather than third side which tells that there are some exceptions
(10,11,21),(10,12,22),(10,11,22) are the 3 exceptions which we have to remove
The number of noncongruent integer-sided triangles are 2863=283

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