Question

The three sides of a triangle measure x - 2, x + 1, and x + 2. Which of the following could x not equal? 19 17 8 4 3

Answer 1

x ≠ 3

Explanation:

difference of 2 shorter sides < the longest side < sum of 2 shorter sides

(x+1) - (x-2) < x+2 < (x+1) + (x-2)

⇔ 3 < x+2 < 2x-1

⇔ 3-2 < x < 2x-1-2

⇔ 1 < x < 2x-3

[1] x > 1

[2] x < 2x-3

x > 3

[1] + [2]

x > 3

Therefore x ≠ 3