Question

Two sides of a triangle are

shown. Find the range of
values of the third side.
23,41
k
< X

Answer 1

By the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So for sides of length 23 and 41, the range of values for the third side, x, would be:

41 - 23 < x < 41 + 23

18 < x < 64

Therefore, the range of values for the third side is 18 < x < 64.