Let $T$ be a triangle with sides of length $a,b,c$ and $T'$ a triangle with sides of length $a',b',c'$. If $a<a'$ and $b<b'$ and $c<c'$, is it true $Area(T)<Area(T')$?
I've tried to use Heron's formula, but I wasn't able to prove this.
2026-03-29 20:32:11.1774816331
Length of sides of a triangle and area
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No, it's wrong! Try, $a=b=c=1$ and $a'=b'=100$ and $c'\rightarrow200^-$.
For example, $c'=199.9999999$ is valid.