Question

1. in triangle abc, the length of side ab is 10 in. and the length of side bc is 17 in. what is the possible lengths for side ac?

a) ( 7 < x < 27 ) b) ( 10 > x > 17 )
c) ( 7 > ac > 27 ) d) ( 10 < x < 17 )

Explanation:

Step1: Apply triangle inequality theorem (difference of two sides)

In a triangle, the length of any side must be greater than the difference of the lengths of the other two sides.
So, \(|AB - BC|\lt AC\), substituting \(AB = 10\) and \(BC=17\), we get \(|10 - 17|\lt AC\), i.e., \(7\lt AC\).

Step2: Apply triangle inequality theorem (sum of two sides)

In a triangle, the length of any side must be less than the sum of the lengths of the other two sides.
So, \(AC\lt AB + BC\), substituting \(AB = 10\) and \(BC = 17\), we get \(AC\lt10 + 17\), i.e., \(AC\lt27\).

Answer:

A. \(7\lt x\lt27\)