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Show that the sum of the three altitudes of a triangle is less than the sum of the three sides of a triangle

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You have to do a activity for it. take a rectangular strip of paper and make it a triangle ABC by folding its sides. now take another strip DE equal to side AB now try to fit it inside the triangle without folding it from anywhere. you'll find that it can't be fitted without folding. it means that that strip should be smaller so that it can be fitted. it means that the altitude is always smaller. repeat it with other sides and you'll get the same answer. now it means that every altitude is smaller than sides. hence sum of all sides of triangle is always bigger than sum of its altitudes.
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