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Prove that the perimeter of a triangle is greater then its three altitudes?
Wiki User
∙ 6y ago
draw a triangle ABC and three altitudes
AH
BL
and CM
AH_|_ BC
BL _|_AC
and CM _|_ AB
for right triangle AHB, using Pythagorean
AH² = AB² - BH²
so AH < AB
similarly for other altitudes
thus
AH+BL+CM is < AB+BC+CA
Wiki User
∙ 6y ago
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