smc

Let $l$ represent the length of one of the smaller rectangles, and let $w$ represent the width of one of the smaller rectangles, with $w<l$. From the large rectangle, we see that the top has length $3w$, the right has length $l+w$, the bottom has length $2l$, and the left has length $l+2$. Since the perimeter of the large rectangle is $176$, we know that $172=3w+l+w+2l+l+w$, or $172=5w+4l$ From the top and bottom of the large rectangle, we know that $3w=2l$, or $l=1.5w$. Plugging that into the first equation, we get $176=5w+4(1.5)w$ $176=11w$ $w=16$ $l=1.5w=24$ $P=2l+2w=2(16+24)=80$, and the answer is $\boxed{80}$