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

Explanation:

Step1: Apply triangle - inequality theorem (sum of two sides)

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, $(2x + 2)+(x + 3)>n$, which simplifies to $3x+5>n$.

Step2: Apply triangle - inequality theorem (difference of two sides)

The difference between the lengths of any two sides of a triangle must be less than the length of the third side. So, $|(2x + 2)-(x + 3)|x - 1$.

Answer:

$x - 1