To find the length of the side of the supply closet labeled with the question mark, we need to first determine the areas of the shapes provided and ensure they total 36 square feet.

Question

You mentioned a rectangle and a square. From the details:

Rectangle:

Length = 8 ft
Width = 3 ft
Area = Length × Width = 8 ft × 3 ft = 24 sq ft
Square:

Side = 2 ft
Area = Side × Side = 2 ft × 2 ft = 4 sq ft
Now, let's add the areas of the rectangle and the square:

Total area of the rectangle + area of the square = 24 sq ft + 4 sq ft = 28 sq ft
Since the total area of the entire supply closet is 36 sq ft, we can determine the area of the remaining part (the area corresponding to the side with the question mark):

Remaining area = Total area - Area of rectangle - Area of square = 36 sq ft - 28 sq ft = 8 sq ft
If we assume that the area corresponding to the side labeled with the question mark is a square, you would need to find the length of a side of that square:

Let the side of the square with the question mark be .
The area of that square =
To find , take the square root of both sides:

≈ 2.83 ft.
Thus, the length in feet of the side of the supply closet labeled with the question mark is approximately:

2.83 feet (if rounded).

If you need a specific format (like 2.82 rounded to two decimal places), please let me know!

Pls don’t round

Answer 1

To find the side length of the supply closet labeled with the question mark, we first confirm the areas already calculated:

1. Area of the rectangle:

   • Length = 8 ft
   • Width = 3 ft
   • Area = Length × Width = 8 ft × 3 ft = 24 sq ft

2. Area of the square:

   • Side = 2 ft
   • Area = Side × Side = 2 ft × 2 ft = 4 sq ft

Next, we add these areas together:

• Total area of the rectangle + area of the square = 24 sq ft + 4 sq ft = 28 sq ft.

Now, we know the total area of the entire supply closet is 36 sq ft, so we can determine the remaining area:

• Remaining area = Total area - Area of rectangle - Area of square
• Remaining area = 36 sq ft - 28 sq ft = 8 sq ft.

We need to find the length of the side of the shape corresponding to this remaining area.

Assuming that this area is a square, we denote the side length of the square as \( x \). The area of that square is:

\[ x^2 = 8 \text{ sq ft} \]

To find \( x \), we take the square root of both sides:

\[ x = \sqrt{8} = 2\sqrt{2} \text{ ft}. \]

To express \( \sqrt{2} \) in decimal form:

\[ \sqrt{2} \approx 1.41421356. \]

Thus:

\[ x \approx 2 \times 1.41421356 \approx 2.82842712 \text{ ft}. \]

Therefore, the length of the side of the supply closet labeled with the question mark is:

\[ 2\sqrt{2} \text{ feet} , \text{or} , 2.82842712 \text{ feet (exact decimal)}. \]

If you require it in a specific format or rounding, please let me know!