SOLUTION: In an equilateral triangle is it possible for the sum of the measures of the altitudes of the triangle be larger than perimeter of the triangle?

Question 547349: In an equilateral triangle is it possible for the sum of the measures of the altitudes of the triangle be larger than perimeter of the triangle?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
No. We are comparing the sum of the lengths of the three (equal) altitudes and the three (equal) sides, so all we need to do is compare one altitude and one side. The side length is longer (it corresponds to the "hypotenuse" of a 30-60-90 triangle) so the perimeter must always be longer than the sum of the altitudes. Hence the statement cannot occur.
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