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
![y+z>x](https://tex.z-dn.net/?f=y%2Bz%3Ex)
![4+z>15](https://tex.z-dn.net/?f=4%2Bz%3E15)
![z>15-4](https://tex.z-dn.net/?f=z%3E15-4)
...(i)
It is clear that
. So, y cannot be a largest side.
Case II: Let z be the largest side, then
![x+y>z](https://tex.z-dn.net/?f=x%2By%3Ez)
![15+4>z](https://tex.z-dn.net/?f=15%2B4%3Ez)
...(ii)
From (i) and (ii), we get
![11](https://tex.z-dn.net/?f=11%3Cz%3C19)
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.