The answer is not 1200

let y be the length of the rectangle and x be the width of the rectangle

we know that y is also the length of the square and y = 3x

2y + 2x = 400

2y + 2(3x) = 400

x = 50

y = 3(50) = 150

P = 4y = 4(150) = 600

At least one of the three rectangles must share a side with the square. Therefore, since they are congruent, they must all be side by side or on top of each other (since each must have one side length equal to the square). This implies that for each rectangle one side must be 1/3 of the length of the other one. Call this side x. Then $x + x + 3x + 3x = 400$ . So, $x = 50$ and the length of the other side $= 3x = 150$ .

So, each rectangle must be $150$ by $50$ . $150$ corresponds to one side of the square, so the perimeter of the square is $150 \cdot 4 = \boxed{600}$

Let each side of the square be 3x.

Since each square is divided into 3 congruent rectangles, their dimensions will be 3x * x

The perimeter of a rectangle = 3x + 3x + x + x = 8x = 400 (given)

hence $\boxed{x=50}$

Perimeter of square = 4 ( 3x) = 12x = $\boxed{600}$

Suppose that the square side is $a,$ so the perimeter of the rectangle equals $2(a+a/3)=400.$ Then $(8/3)a=400,$ so $a=150.$ Then the square perimeter equals $4a=4(150)=600.$

$perimeter~of~one~rectangle=2(3x)+2x=6x+2x=8x$

$400=8x$

$x=\dfrac{400}{8}=50$

$perimeter~of~the~square=4(3x)=12x=12(50)=$ $\color{#D61F06}\boxed{600}$

Consider the given statements. All the rectangles are congruent, so one side of the rectangle has to be a side of the square (imagine two identical cuts of the square parallel to one side of the square to get the three rectangles). Then we have that the perimeter is 400, so the sum of the two side lengths of a given rectangle is 200. Furthermore, the short side of the rectangle must be 3 times longer than the long side since we have 3 congruent rectangles. Thus we have a system

y = 3x x + y = 200

Substitute and find that x = 50. Trivially, the square side length must be longer than the short side of the square, so the square side length is 200 - x = 150. Then 4x = perimeter of square = 600.

The side of rectangle has 1:3 as their proportion. Because of the perimeter, the sum of its side is 200. So, the longer side of rectangle which is side of square is 200.3/4=150. So, the perimeter of square is 4.150=600