Question

In triangle ABC, AB = 15.5 cm and BC = 7.5 cm.
Then ___ < AC < ____.

• A. 8, 23
• B. 9, 31
• C. 15, 24
• D. 9, 23

Answer 1

The correct option is A 8, 23

By triangle inequality, sum of any two sides of a triangle is greater than the third side.
Let the third side in the given triangle be 'x'.
x should be less than $15.5+7.5$.
$x<15.5+7.5x<23$
15.5 should be less than $x+7.5$.
$15.5<x+7.515.5-7.5<xx>8$
So, $8<x<23$.