A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side is 3 feet. Corners are marked with right angles.

Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?(1 point)

__feet

1 answer

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.

  1. The total area of the closet is given as 36 square feet.
  2. 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.
  3. 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: \[ \boxed{18} \text{ feet} \]