Let's draw a triangle â–ł ABC with the given sides AB=5 and BC=11.
We are asked to find the range of possible length of side CA.
Since AB, BC, and CA are three sides of a triangle, we can use the Triangle Inequality Theorem to get bounds for CA.
The sum of the length of any two sides of a triangle
is greater than the length of the third side.
The key word here is any. This theorem gives restriction on the length of the sides in three ways.
Inequality
Consequence
AB+ BC&> CA 5+ 11&> CA
CA< 5+ 11=16
BC+ CA&> AB 11+ CA&> 5
Always true
CA+ AB&> BC CA+ 5&> 11
CA> 11- 5=6
Notice that since 11> 5, the second inequality is always true. The first inequality tells us that CA cannot be too long, and the third inequality tells that CA cannot be too short.
6< CA< 16
The correct answer choice is H.
