## How to Cut a Rectangle in Three With Parallel Lines to Give Three Equal Areas

Draw a vertical line from G to the top side at P

then

\[tan 45=\frac{PB}{PG} \rightarrow 1=\frac{PB}{4}\rightarrow PB=4\]

Then

\[AB=x+4\]

By syymetry,

\[EF=x+4\]

and then \[FG=10-(x+x+4)=6-2x\]

The areas of ABGH and BCFG are equal.

\[\frac{1}{2}(x+x+4)(4)=(6-2x)(4) \rightarrow x+2=6-2x \rightarrow 3x=3x=4 \rightarrow x=\frac{4}{3}\]