Question

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

• A. $283$
• B. $446$
• C. $448$
• D. $449$

Answer 1

Answer: (A)

$283$

For the scalene triangle , select any three sides from the set which can be done in ${}^{13}{C}_3=286$ 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 $286-3=283$