Question

What are the two possible min and max values (range) for the length of the third side?

Answer 1

ANSWER: 16 > x > 38

Rule: The sum of two smaller sides is greater than the largest side.

You can assume that 27 is the largest side.

x + 11 > 27
x > 16

or

You can assume that ‘x’ is the largest side (because it’s actual value as not been determined yet).

11 + 27 > x
x < 38

BUT, you CANNOT assume that 11 is the largest side because it does not follow the rule (11 is not larger than 27).

All in all, you would end up w/ this Triangle
Inequality:

16 > x > 38

Answer 2

16 and 38

Explanation:

Given 2 sides of a triangle then the third side x

difference of 2 sides < x < sum of 2 sides , that is

27 - 11 < x < 27 + 11

16 < x < 38