Problema Solution
the sum of the length of any two sides of a triangle mus be greater than the third side. if a triangle has one side that is to inches and a second side that is 2 inches less than twice the third side, what are the possible lengths for the second and third sides?
Answer provided by our tutors
the problem statement is ambiguous; we assume that "one side that is to inches" is interpreted as "one side that is 2 inches"
let 'x' represent the third side, then the second side is interpreted as "2x-2", which is 2 inches less than twice the third side
so the three sides are 2, 2x-2 and x
the sum of the three sides would be 2+(2x-2)+x
the sum of any two sides could be 2+x, (2x-2)+x or(2x-2)+2
x>0
x>4/3
x<4
The problem statement is asking for an inequality but solving for an inequality shows two possible sides of 4 and 4/3 but the sums of 2 and (2x-2) will be greater than 'x' other than x=4/3, hence this is ambiguous because x=0 is not an allowable length.