+118629 I do not ever remember seeing a question like this before :)
ratio of 5 to 4 with product of 81
Let the numbers be (5x/9) and (4x/9)
This has nothing to do with the 81. The nine comes from 4+5=9
\(\frac{5x}{9}\times \frac{4x}{9}=81\\ \frac{20x^2}{81}=81\\ 20x^2=81^2\\ 20x^2=6561\\ x^2=328.05\\ x=\sqrt{32805}\div10\)
factor(32805) = 3^8*5
\(x=\frac{\sqrt{81*81*5}}{10}\\ x=\frac{81\sqrt{5}}{10}\\\)
so the numbers are
\(\frac{5}{9}\;of\; 8.1\sqrt5 \quad and \qquad \frac{4}{9}\;of\; 8.1\sqrt5\\ \quad4.5\sqrt5 \qquad and \qquad 3.6\sqrt5\\\)
check
4.5*sqrt(5)*3.6*sqrt(5) = 81
and
4.5*sqrt(5)/(3.6*sqrt(5)) = 1.25 = 5/4
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