Two sides of scalene Triangle ABC measure 3 centimeters and 5 centimeters. How many different whole centimeter lengths are possible for the third side?
Let the unknown side = S
By the triangle inequality
S < 3 + 5
S < 8
S + 3 > 5
S > 2
And
S + 5 < 3
S > -2
But taking the most restrictive interval
2 < S < 8
But since the triangle is scalene.....then the possible lengths for S are 4, 6, and 7 (cm)
CPhill i think you meant S+5>3
