KVPY Sample Paper KVPY Stream-SX Model Paper-13

The number of triangles with each side having integral length and the longest side is of 11 units is

A) 30

B) 34

C) 35

D) 36

Correct Answer: D

Solution :

Let the three sides of triangle are a, b and c.

\[a\le b\le c=11\]

\[\therefore \] \[6\le b\le 11\]and \[c-b<a\le b.\]

As b decreased by 1 unit the range of a decreased by 2 when b =11, we have

\[1\le a\le 11\]

Hence, the total number of triangle is

\[11+9+7+5+3+1=36\]