SOLUTION: Given △ABC. m∠A>m∠B>m∠C. Perimeter of ABC=30. Which one of the three sides may have length 7?

Question 1132585: Given △ABC. m∠A>m∠B>m∠C. Perimeter of ABC=30. Which one of the three sides may have length 7?

Answer by ikleyn(53765) (Show Source): You can put this solution on YOUR website!
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Notice that the given triangle is a scalene triangle: it has no congruent sides.


Since 3 times 7 is 21, the side of the length 7 can not be longest.


If the side of the length 7 is the middle length side, then there is the shorter side; 
but then the third side has the length greater than 30-2*7 = 16.

It contradicts to the triangle inequality.


Thus the side of the length 7 is with necessity the shortest side of the triangle.


In any triangle, the shortest side is opposite to the smallest angle.


Hence, the side of the length 7 in the given triangle is opposite to the angle C.

Solved.

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