Question

a triangle has sides measuring 8 inches and 12 inches. if x represents the length in inches of the third side, which inequality gives the range of possible values for x?
a. 4≤x≤20
b. 4<x<20
c. 8≤x≤12
d. 8<x<12

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. So \(x + 8>12\), \(x+12 > 8\) (which is always true for non - negative \(x\)), and \(8 + 12>x\).
From \(x + 8>12\), we get \(x>12 - 8\), so \(x>4\).
From \(8 + 12>x\), we get \(x<20\).

Answer:

B. \(4 < x<20\)