Question 884695
{{{(1/2)AB=30}}}
{{{AB=60}}}
.
.
{{{A^2+B^2=13^2}}}
{{{A^2+B^2=169}}}
From the first equation,
{{{A=60/B}}}
Substitute,
{{{(60/B)^2+B^2=169}}}
{{{3600/B^2+B^2=169}}}
{{{3600+B^4=169B^2}}}
{{{B^4-169B^2+3600=0}}}
{{{(B^2-17B+60)(B^2+17B+60)=0}}}
{{{(B-5)(B-12)(B+5)(B+12)=0}}}
Only the positive solution works here.
Two solutions:
{{{B-5=0}}}
{{{B=5}}}
Then,
{{{A=60/5}}}
{{{A=12}}}
and
{{{B-12=0}}}
{{{B=12}}}
Then,
{{{A=60/12}}}
{{{A=5}}}