<s>[INST] Area inside a rectangle 
SEAMO 2016 paper E
I do not know how to start with this question and I have tried finding heights and bases of the triangle in terms of the sides of rectangle but i could not find the ideal pair
 [/INST] Let $AC\cap EG=\{H\}$ and $AC\cap GF=\{I\}$.
Thus, $$\frac{AH}{HC}=\frac{AE}{GC}=\frac{\frac{1}{3}}{\frac{1}{2}}=\frac{2}{3},$$
Which says that $$AH=\frac{2}{5}AC.$$
Also,
$$\frac{CI}{IA}=\frac{CG}{AF}=\frac{\frac{1}{2}}{\frac{2}{3}}=\frac{3}{4},$$
Which says that $$CI=\frac{3}{7}AC.$$
Thus, $$HI=AC\left(1-\frac{3}{7}-\frac{2}{5}\right)=\frac{6}{35}AC,$$
which says
$$\frac{S_{\Delta IHG}}{S_{\Delta ADC}}=\frac{6}{35}\cdot\frac{1}{2}=\frac{3}{35}$$ and
$$S_{\Delta IHG}=\frac{3}{70}S_{ABCD}=1.5.$$
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