Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.
In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:
l + 2x = 3w
In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:
l = 2(w + x)
We now have two equations with two unknowns, l and w:
l + 2x = 3w
l = 2(w + x)
Substituting the second equation into the first, we get:
2(w + x) + 2x = 3w
4x = w
Substituting this value of w into the second equation, we get:
l = 2(4x) = 8x
So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.
To find the value of x, we use the measurements given in the diagram:
l + 2x = 60
l = 36
Substituting into the equation l = 2(w + x), we get:
36 = 2(4x + x)
36 = 10x
x = 3.6
So the side length of the square rug is 3.6 feet.
Explanation: