anonymous
  • anonymous
Prove that in any triangle the length of a side is less than half of the perimeter.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Lets consider a Triangle with area greater than Zero (obviously :/) \[\sqrt{s(s-a)(s-b)(s-c)} = Area \implies Area^2 = s(s-a)(s-b)(s-c) \] If Area > 0 \(\implies \) \(Area^2 > 0\). \[s(s - a)(s-b)(s-c)> 0 \] Note. s is the half perimeter.
anonymous
  • anonymous
I have never ever done this problem before ...So ... DO NOT TRUST ME.
anonymous
  • anonymous
Lets not square it, okay? \[\sqrt{s(s-a)(s-b)(s-c)} > 0\] s = (a+b+c)/2 \[\sqrt{2s(2s-2a)(2s-2b)(2s-2c)} > 0\]\[\sqrt{(a+b+c)(b + c - a)(a+b-c)(a+c - b)} >0\] For a triangle, third side can not be greater than the sum of the other two sides.

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anonymous
  • anonymous
is it right?
anonymous
  • anonymous
yes it is
amistre64
  • amistre64
what does area have to di with perimeter?
amistre64
  • amistre64
id prove it for an equitri and asses it from there
amistre64
  • amistre64
i see you used heron for relating sides ...
anonymous
  • anonymous
a+b>c a+b+c>2c (a+b+c)/2 > c
anonymous
  • anonymous
pssstt... i am still not sure if it's a conclusive proof, just made it out of thin air :/
anonymous
  • anonymous
oh foolformath completed it
amistre64
  • amistre64
how many assumptions are we allowed to make? fool used a thrm for a proposition i think
anonymous
  • anonymous
a + b > c a+ b - c + c -c>0 2s - 2c > 0 s > c same can be done for every side
anonymous
  • anonymous
Sum of any two sides of a triangle is greater than the third side. http://www.proofwiki.org/wiki/Sum_of_Two_Sides_of_Triangle_Greater_than_Third_Side

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