Question

If side x has a length of 15 cm and side y has a length of 4 cm, then which value below could be the length of side z?

A.
20 cm
B.
21 cm
C.
17 cm
D.
10 cm

Answer 1

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`

`4+z>15`

`z>15-4`

`z>11` ...(i)

It is clear that
`y<x`. So, y cannot be a largest side.

Case II: Let z be the largest side, then

`x+y>z`

`15+4>z`

`19>z` ...(ii)

From (i) and (ii), we get

`11<z<19`

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.