Stacking Rectangles

Relevant wiki: Length and Area Problem Solving

Let the length and breadth of each smaller rectangles be $x$ and $y$ respectively. Now look at the length of big rectangle in the figure, it is represented by $4x$ and $3y$ both so you get $4x=3y$ . And the breadth of bigger rectangle is $x+y$ . Since it perimeter is 76 we get $2((x+y)+(3y))=76$ or $x+4y=38$ , solving these two equation gives $x=6,y=8$ and we want is $2(6+8)=\boxed{28}$ .

Let W and w, and L and l be the width and length of big and small rectangles respectively.
From middle horizontal line we see 3l=4w. That is w=3/4l.
W=w+l. ... L=3l.
W+L=76/2=38=w+4l=4.75l.
So 38=19/4 * l, and l=8. So w=3/4 * 8=6.
So 2(w+l)=2(6+8)= 28 .

Let $l$ be the length and $w$ be the width.
$6l + 5w = 76$
Assuming integer lengths Multiple of 6 + Multiple of 5 = 76 To make an even sum, $5w$ has to end with 0 not 5 as it requires 2 even or 2 odd to make an even and $6l$ is always even, thus $6l$ has to end with 6 making it 6 or 36 or 66 $76 = 6 + 70 , 36 + 40 , 66 + 10$ Based on the rough scale of the diagram The pair has to be 36 and 40, making $w = 6$ and $l = 8$ $\therefore 2w + 2l = 12 + 16 = \boxed{28}$