To find the length of the side of the supply closet labeled with the question mark, let's first summarize the information provided.
- The area of the entire rectangular shape is 36 square feet.
- There's a rectangular area that is 8 feet long and has an unknown width that is removed from the bottom left corner.
- The remaining rectangle on the right has a height of 2 feet and a width of 3 feet.
Step 1: Calculate the area of the rectangle that remains after the cut-out.
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The area of the remaining rectangle (on the right side) is given by the formula: Area = Length × Width Here, the remaining length is 2 feet and the remaining width is 3 feet.
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Area = \( 2 , \text{feet} \times 3 , \text{feet} = 6 , \text{square feet} \).
Step 2: Determine the total area of the entire rectangular shape.
- The total area is 36 square feet (from the problem description).
Step 3: Calculate the area of the cut-out rectangle.
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Given that the area of the remaining rectangle is 6 square feet, the area of the cut-out rectangle is:
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Area of cut-out rectangle = Total area - Area of remaining rectangle
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Area of cut-out rectangle = \( 36 , \text{square feet} - 6 , \text{square feet} = 30 , \text{square feet} \).
Step 4: Use the dimensions of the cut-out rectangle to find the unknown width.
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The area of the cut-out rectangle is also equal to its length (8 feet) multiplied by its width (w):
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\( 8 , \text{feet} \times w = 30 , \text{square feet} \).
Now, solve for w: \[ w = \frac{30 , \text{square feet}}{8 , \text{feet}} = 3.75 , \text{feet} \]
The unknown width of the cut-out part is 3.75 feet.
Step 5: Determine the total height of the original closet with the dimensions given.
The total height before the cut-out at the left side was divided into:
- The cut out width is 3.75 feet, and the remaining is 2 feet. Thus, the total height = height of cut out + height of remaining part = 3.75 + 2 = 5.75 feet. (However, for rectangle area calculation, rearanging layout with sufficient drawing should make it seem the unknown side is what we are working with hence considering the additional orientation layout as measured from what’s left.)
Now, return to understanding the total rectangle area relationship since dimensions aren't showing prints etc.
However, if close to bottom reflects the original nature at foot heights: [ \text{Length with question mark} (h) + \text{set remaining (3 ft)}\times \text{Width} (2 ft) yield alongside confirms width in another contextual measure.
Summarizing up: The length on the dimension side with question should holds onto be equal structured for new area formed == hold as remaindering altogether unspent whilst observing its constraints, gives the balanced alter alongside 3 ft width-maintained as the final query being simply put as the proximal portion holding together balance.
Therefore, the answer for the side of the supply closet labeled with the question mark is 3.75 feet.
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