Let $l$ be the given line and let $l'$ be the line perpendicular to $l$. Note that each side of covering rectangles is parallel to one of the lines $l$ and $l'$. Now let $P$ be any interior point of the given triangle $T$ (assume that $T$ is set of all points on sides of triangle). Let $t$ and $t'$ be the lines such that $P=t\cap t'$ and $t||l$ and $t'||l'$. Let $S=\{U,V,W,Z\}=(T\cap t)\cup (T\cap t')$. Since we have $3$ rectangles one of them, say $R$, will contain at least two points from the set $S$ and now it is obvious that $R$ will contain $P$.