Let's denote the side length of the square as $ s $. Since the square is divided into five congruent rectangles, each rectangle will have the same dimensions. Let the dimensions of each rectangle be $ l $ (length) and $ w $ (width).

Since the rectangles are congruent and fit perfectly within the square, the total area of the square is equal to the sum of the areas of the five rectangles. Therefore, we have:
$$ s^2 = 5lw $$

Given that the perimeter of each rectangle is $ P $ inches, we can express this as:
$$ P = 2l + 2w $$

We need to find the perimeter of the square, which is $ 4s $.

First, let's express $ l $ and $ w $ in terms of $ s $. Since the rectangles are congruent and fit within the square, we can consider two possible configurations:
1. The rectangles are arranged side by side horizontally.
2. The rectangles are arranged one above the other vertically.

### Case 1: Rectangles arranged horizontally
In this case, the width $ w $ of each rectangle is equal to the side length of the square divided by 5:
$$ w = \frac{s}{5} $$

The length $ l $ of each rectangle is equal to the side length of the square:
$$ l = s $$

Substituting these into the perimeter formula for the rectangle:
$$ P = 2l + 2w = 2s + 2\left(\frac{s}{5}\right) = 2s + \frac{2s}{5} = 2s + 0.4s = 2.4s $$

Given that $ P $ is the perimeter of each rectangle, we have:
$$ P = 2.4s $$

### Case 2: Rectangles arranged vertically
In this case, the length $ l $ of each rectangle is equal to the side length of the square divided by 5:
$$ l = \frac{s}{5} $$

The width $ w $ of each rectangle is equal to the side length of the square:
$$ w = s $$

Substituting these into the perimeter formula for the rectangle:
$$ P = 2l + 2w = 2\left(\frac{s}{5}\right) + 2s = \frac{2s}{5} + 2s = 0.4s + 2s = 2.4s $$

Given that $ P $ is the perimeter of each rectangle, we have:
$$ P = 2.4s $$

In both cases, we find that:
$$ P = 2.4s $$

To find the side length $ s $ of the square, we solve for $ s $:
$$ s = \frac{P}{2.4} $$

Finally, the perimeter of the square is:
$$ 4s = 4 \left(\frac{P}{2.4}\right) = \frac{4P}{2.4} = \frac{4P}{2.4} = \frac{5P}{3} $$

Therefore, the perimeter of the square is:
$$ \boxed{\frac{5P}{3}} $$

Question

Let's denote the side length of the square as $ s $. Since the square is divided into five congruent rectangles, each rectangle will have the same dimensions. Let the dimensions of each rectangle be $ l $ (length) and $ w $ (width).

Since the rectangles are congruent and fit perfectly within the square, the total area of the square is equal to the sum of the areas of the five rectangles. Therefore, we have:
$$ s^2 = 5lw $$

Given that the perimeter of each rectangle is $ P $ inches, we can express this as:
$$ P = 2l + 2w $$

We need to find the perimeter of the square, which is $ 4s $.

First, let's express $ l $ and $ w $ in terms of $ s $. Since the rectangles are congruent and fit within the square, we can consider two possible configurations:
1. The rectangles are arranged side by side horizontally.
2. The rectangles are arranged one above the other vertically.

### Case 1: Rectangles arranged horizontally
In this case, the width $ w $ of each rectangle is equal to the side length of the square divided by 5:
$$ w = \frac{s}{5} $$

The length $ l $ of each rectangle is equal to the side length of the square:
$$ l = s $$

Substituting these into the perimeter formula for the rectangle:
$$ P = 2l + 2w = 2s + 2\left(\frac{s}{5}\right) = 2s + \frac{2s}{5} = 2s + 0.4s = 2.4s $$

Given that $ P $ is the perimeter of each rectangle, we have:
$$ P = 2.4s $$

### Case 2: Rectangles arranged vertically
In this case, the length $ l $ of each rectangle is equal to the side length of the square divided by 5:
$$ l = \frac{s}{5} $$

The width $ w $ of each rectangle is equal to the side length of the square:
$$ w = s $$

Substituting these into the perimeter formula for the rectangle:
$$ P = 2l + 2w = 2\left(\frac{s}{5}\right) + 2s = \frac{2s}{5} + 2s = 0.4s + 2s = 2.4s $$

Given that $ P $ is the perimeter of each rectangle, we have:
$$ P = 2.4s $$

In both cases, we find that:
$$ P = 2.4s $$

To find the side length $ s $ of the square, we solve for $ s $:
$$ s = \frac{P}{2.4} $$

Finally, the perimeter of the square is:
$$ 4s = 4 \left(\frac{P}{2.4}\right) = \frac{4P}{2.4} = \frac{4P}{2.4} = \frac{5P}{3} $$

Therefore, the perimeter of the square is:
$$ \boxed{\frac{5P}{3}} $$

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