Question

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft.

Which expression represents the possible values of n, in feet? Express your answer in simplest terms.

x – 1 < n < 3x + 5
n = 3x + 5
n = x – 1
3x + 5 < n < x – 1

Answer 1

Use the triangle inequalities:
n < (2x+2)+(x+3) = 3x+5
and
n > |(2x+2)-(x+3)| = |x-1| = x-1 (assuming x≥1 so side lengths positive).

Thus x – 1 < n < 3x + 5.