a triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft. which expression represents the…

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. o x - 1 < n < 3x + 5 o n = 3x + 5 o n = x - 1 o 3x + 5 < n < x - 1

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. o x - 1 < n < 3x + 5 o n = 3x + 5 o n = x - 1 o 3x + 5 < n < x - 1

Answer

Explanation:

Step1: Apply 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.

  1. First, consider $(2x + 2)+(x + 3)>n$, which simplifies to $3x+5>n$.
  2. Second, consider $(2x + 2)+n>(x + 3)$, which simplifies to $n>x + 3-(2x + 2)=x + 3-2x - 2=-x + 1$.
  3. Third, consider $(x + 3)+n>(2x + 2)$, which simplifies to $n>2x + 2-(x + 3)=2x+2 - x - 3=x - 1$. Combining the inequalities, we get $x - 1 < n<3x + 5$.

Answer:

A. $x - 1 < n<3x + 5$