Points $E$ and $F$ are on sides $AB$ and $BC$ of rectangle $ABCD$ so that: $S_{ADE}=5,S_{CDF}=3,S_{BEF}=8$.Calculate the area of triangle $DEF$($S_{DEF}$)
I just could write a relation between areas of all triangles taking into account length and width of rectangle,but nothing more...
\begin{eqnarray} 10 &=& AE.AD\\ 6 &=& DC.FC\\ 16 &=& BE.BF=(DC-AE)(AD-FC) \end{eqnarray} then from third $$16 = (DC-\frac{10}{AD})(AD-\frac{6}{CD})$$ with $AD=x$ and $CD=y$ we get $$(xy)^2-32(xy)+60=0$$ then two answers obtain $$S_1=\frac12xy=1$$ $$S_2=\frac12xy=15$$