Question

two sides of a triangle are 14 and 15.8. find the range of possible side lengths for the third side. type your answer as an inequality with appropriate symbols, using x as your variable. type your answer as an inequality like we did in the notes with appropriate symbols, using x as your variable.

Explanation:

Step1: Recall 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. Let the sides of the triangle be \(a = 14\), \(b=15.8\), and \(x\) be the third - side. Then \(a + x>b\), \(x + b>a\), and \(a + b>x\).

Step2: First inequality \(a + x>b\)

\(14 + x>15.8\), which simplifies to \(x>15.8 - 14\), so \(x > 1.8\).

Step3: Second inequality \(x + b>a\)

\(x+15.8>14\), which is always true for non - negative values of \(x\).

Step4: Third inequality \(a + b>x\)

\(14 + 15.8>x\), so \(x<29.8\).

Answer:

\(1.8 < x < 29.8\)