An isosceles triangle has at least two congruent sides. The perimeter of a certian isosceles triangle is at most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the remaning side?

Answer 1

Let $s$ be the length of the remaining side. If we attempt to set up the perimeter, we get $5+5+s<12 \Rightarrow 10+s<12 \Rightarrow s<2,$ so our remaining side must be less than $2$ inches in length. However, if we set our remaining side to have length $0,1,$ or $2$ inches, the triangle would degenerate into a line segment and not exist at all, so our possible answer is $\boxed{}$ None.