To find the length of the side of the supply closet labeled with a question mark, we first need to gather and organize the information provided.
- The total area of the closet is given as 36 square feet.
- We know the remaining dimensions of the closet:
- The remaining length on the right side is 2 feet.
- The remaining width on the left side is 3 feet.
- Next, we need to determine what area these dimensions represent.
Let:
- The unknown width of the original rectangle before the cutout be \( w \).
- The total height of the original rectangle be determined by the length and width of the rectangle (the height is still not specified).
From the remaining clues:
- The remaining area after cutting out the rectangle of 8 feet length is 36 square feet.
- The area of a rectangle is calculated as: \[ \text{Area} = \text{Length} \times \text{Width} \]
Since we only have the two dimensions of interest, we can write: \[ \text{Area} = 2 \times (8 + x) \] Where \( x \) is the 8 feet length minus the cutout length.
To help solve it, we can say: \[ 36 \text{ square feet} = (2 \text{ feet}) \times (\text{width}) \]
Now to calculate \( x \): Let \( x \) be the unknown length: \[ 36 = 2 \times x \] Now solve for \( x \): \[ x = \frac{36}{2} = 18 \text{ feet} \]
So the length of the side of the supply closet labeled with the question mark is: \[ \boxed{18} \text{ feet} \]