Question

multiple choice 4 points
the lengths of three sides of a triangle are 5, 9, and x, all measured in centimeters.
what are all possible values of x?
0 < x < 14 5 < x < 15 4 < x < 14 3 < x < 9
multiple choice 4 points
jennies math tutor drew three lines to create a right angle scalene triangle in her
math notebook.
which of the following are the possible whole number lengths of the three segments?
33,35,48 2,3,4 7,24,25 16,17,23

Explanation:

Step1: Apply triangle inequality theorem

For a triangle with side lengths \(a\), \(b\), \(c\), the following must hold: \(a + b>c\), \(a + c>b\), \(b + c>a\). Here \(a = 5\), \(b=9\), \(c=x\).
So \(5 + 9>x\) (i.e., \(x<14\)) and \(5+x>9\) (i.e., \(x > 4\)) and \(9+x>5\) (always true for positive \(x\)).

Answer:

\(4 < x < 14\)