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

Explanation:

Step1: Use triangle inequality theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, \(n<(2x + 2)+(x + 3)\) and \(n>(2x + 2)-(x + 3)\).

Step2: Simplify the inequalities

For \(n<(2x + 2)+(x + 3)\), we have \(n<3x+5\).
For \(n>(2x + 2)-(x + 3)\), \(n>2x + 2-x - 3\), which simplifies to \(n>x - 1\).

Answer:

\(x - 1