SOLUTION: A certain triangle has two angles that have the same measure. if the lengths of the sides of the triangle are 50 and 30, what is the least possible value for the perimeter of the t

Question 246345: A certain triangle has two angles that have the same measure. if the lengths of the sides of the triangle are 50 and 30, what is the least possible value for the perimeter of the triangle?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If two sides are 30 and 50, and two sides are equal, then the third side is either 30 or 50. If the third side is 30, then the triangle exists, since the longest side is less than the sum of the other two sides. The perimeter would be 30+30+50 =110.

The other possibility would be that the third side is 50, but this is not the SMALLEST perimeter possible.

Note that you DO have to make sure the triangle exists. For example, if the problem had been given with sides of 10 and 50, then the equal sides of 10 each would be a 10, 10, 50--this is NOT a triangle, since the longest side must be less than the sum of the other sides.

Dr. Robert J. Rapalje, Retired
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