geometry
posted by dee .
If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

You know that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
So, the other two sides must be at least 11. That means each of the two congruent sides must be at least 6.