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

Answer

Explanation:

Step1: Apply triangle - inequality theorem

The triangle - inequality theorem states that for a triangle with side lengths (a), (b), and (c), (|a - b|\lt c\lt a + b). Let (a=2x + 2) and (b=x + 3). First, find (a + b): (a + b=(2x + 2)+(x + 3)) (=2x+x+2 + 3) (=3x + 5) Second, find (|a - b|): (a-b=(2x + 2)-(x + 3)) (=2x+2-x - 3) (=x-1)

Answer:

(x - 1\lt n\lt3x + 5)