The lengths of two sides of a triangle are 33 units and 42 units. The third side also has an integral length. What is the least possible number of units in the perimeter of the triangle?
By the triangle inequality we have that
S + 33 > 42 where S is the shortest side
Subtract 33 from each side
S > 9 units
So...since the shortest side has an integer length.....this length must be 10 units
So....the least perimeter is 10 + 33 + 42 = 85 units
