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

Step-by-step solution

Number of scalene triangles array l = ¹³ C ₃-3 =283 array array l 10,11,22 10,12,22 10,11,21 array Number of isosceles triangles = ( ¹³ C ₂ 2 )-4 array l 10,10,22 11,11,22 =152 array . Number of equilateral triangles = ¹³ C ₁=13 So total number of triangles =448