KVPY SX SB Exam 2016 Question Paper

Question : 19 of 120

Marks: +1, -0

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

Solution:

Number of scalene triangles

=^13C_3-3=283\{\table 10,11,22;10,12,22;10,11,21\}

Number of isosceles triangles

=(^13C_2×2)-4=152\{\table 10,10,22;11,11,22;10,10,21;10,10,20

Number of equilateral triangles

=^13C_1=13

So total number of triangles = 448

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