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the shortest side of triangle ABC is half of the second side and a third of the longest side. How does the perimeter of the triangle compare to the longest side?
x = the shortest side of triangle ABC ; y = the second side of triangle ABC; z = the longest site of triangle ABC ; P = the perimeter of triangle ABC ;
x = ( 1 / 2 )y; x = ( 1 / 3 )z; Then ( 1 / 2 )y = ( 1 / 3 )z; y = 2z / 3 ; P = x + y + z = ( 1 / 3)z + 2z / 3 + z = z / 3 + 2z / 3 + z = 3z / 3 + z = z + z = 2z ; But 2z > z ; then, P > z ;
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