Given:
In a triangle, side x has a length of 15 cm and side y has a length of 4 cm.
To find:
The possible value of side z.
Solution:
In a triangle, the sum of two smaller sides must be greater than the largest side otherwise the triangle is not possible.
Case I: Let x be the largest side, then
[tex]y+z>x[/tex]
[tex]4+z>15[/tex]
[tex]z>15-4[/tex]
[tex]z>11[/tex] ...(i)
It is clear that [tex]y<x[/tex]. So, y cannot be a largest side.
Case II: Let z be the largest side, then
[tex]x+y>z[/tex]
[tex]15+4>z[/tex]
[tex]19>z[/tex] ...(ii)
From (i) and (ii), we get
[tex]11<z<19[/tex]
It means the value of z lies between 11 and 19.
From the given options, only 17 is the value which lies between 11 and 19. So, the possible length of side z is 17 cm.
Therefore, the correct option is C.