b Change either the longest side or any of the smallest and middle sides.
A
a See solution.
B
bExample Solution: 1, 5, and 55
Practice makes perfect
a According to the Triangle Inequality Theorem, the sum of a triangle's middle side and smallest side must be greater than the longest side. From the exercise, we know that the triangle has the following sides.
Smallest side:& 1
Middle side:& 5
Longest side:& 6
Since 1+5≯ 6, Kelly is correct and the triangle is impossible.
b To make a possible triangle we can change the longest side so that it is between 5 and 6 or we can increase either the smallest or middle side so that their sum is greater than 6.
Smallest side:& 1
Middle side:& 5
Longest side:& 5.5
Since 1+5> 5.5, this is a possible triangle. Note that this is just one possible solution.
