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Answer:

P = 35 cm

Step-by-step explanation:

Rectangles

Being x and y the dimensions of a rectangle, the perimeter can be calculated as:

P = 2x + 2y

The smaller rectangles of the figure have a width of x cm. We don't know the value of the length, but we can see how the two smaller horizontal rectangles' widths complete the height of the vertical rectangle. Since all the rectangles are identical, then the height of each rectangle is

y = 2x

Substituting in the formula and knowing the perimeter is 21:

2x + 2(2x) = 21

6x = 21

x = 21/6 = 7/2 = 3.5

The large rectangle has a width of 2x and a length of y+x = 3x, thus the perimeter is:

P = 2(2x) + 2(3x) = 4x + 6x = 10x

Since x=3.5 cm:

P = 35 cm

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