If ${\Delta }_1,{\Delta }_2$ are the areas of incircle and circumcircle of a triangle with sides 3,4 and 5 then $\frac{{\Delta }_1}{{\Delta }_2}=$ 

$a=3,b=4,c=5$ are sides of right angle triangle

$r=\frac{\Delta }{s}=\frac{\frac{1}{2}ab}{\frac{a+b+c}{2}}=\frac{3\left(4\right)}{3+4+5}=1$

$R=\frac{hypotenuse}{2}=\frac{5}{2}$

$\therefore \frac{{\Delta }_1}{{\Delta }_2}=\frac{\pi r^2}{\pi R^2}=\frac{{\left(1\right)}^2}{{\left(\frac{5}{2}\right)}^2}=\frac{4}{25}$