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jmc

geometry intermediate

Problem

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?
Solution
The sum of the smaller two sides must exceed the greatest side, so if is the missing side then . The smallest integer greater than 9 is 10, so the least perimeter is units.
Final answer
85