Question

A triangle has sides 6, 11, and x. which of the following is the perimeter of the triangle?

a) 17
b) 18
c) 22
d) 30
e) 34

Answer 1

The perimeter of the triangle must be 30.

We can tell this because when we add two sides of a triangle together, it must be greater than the 3rd side. This is true for all triangles.

a. will not work because the 3rd side would have to be 0, which is not possible.

c. will not work because the 3rd side would have to be 1. This will not create a triangle because 1 + 6 is not greater than 11.

c. will not work because the 3rd side would have to be 5. This will not create a triangle because 5 + 6 is not greater than 11.

d. will not work because the 3rd side would have to be 17. This will not create a triangle because 11 + 6 is not greater than 17.

This leaves us with just d. This perimeter works because the 3rd side would be 13, and 6 + 11 is greater than 13. Therefore, it is the only possible answer.