Question 316471
Use Heron's theorem,
{{{s=(1/2)(a+b+c)=(1/2)(5+12+13)=15}}}
{{{A=sqrt(s(s-a)(s-b)(s-c))}}}
{{{A=sqrt(15(15-5)(15-12)(15-13))}}}
{{{A=sqrt(15(10)(3)(2))}}}
{{{A=sqrt(900)}}}
{{{highlight(A=30)}}}
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Then use the area of a triangle,
{{{A=(1/2)bh=30}}}
Smallest h would have the largest b.
Use b=13.
{{{(1/2)(13)h=30}}}
{{{highlight(h=60/13)}}}