To divide the bookstore space into three sections—nonfiction, novels, and stationary—let's first determine how much space each section will occupy.
- Total Space: The total space of the bookstore is 288 ft².
- Stationary Section: The bookstore wants to allocate \( \frac{1}{3} \) of its space to the stationary section.
Calculating the area of the stationary section:
\[ \text{Area of stationary section} = \frac{1}{3} \times 288 , \text{ft}^2 = 96 , \text{ft}^2 \]
Since the stationary section is given to be 12 feet wide, we can find its length using the formula for the area of a rectangle (Area = Width × Length):
\[ \text{Area} = \text{Width} \times \text{Length} \]
Substituting the known values into the equation:
\[ 96 , \text{ft}^2 = 12 , \text{ft} \times \text{Length} \]
Now, solve for the length:
\[ \text{Length} = \frac{96 , \text{ft}^2}{12 , \text{ft}} = 8 , \text{ft} \]
So, the stationary section will have dimensions:
- Width: 12 ft
- Length: 8 ft
- Remaining Space: Since 1/3 of the total area is allocated to the stationary section, the remaining area for nonfiction and novels is:
\[ 288 , \text{ft}^2 - 96 , \text{ft}^2 = 192 , \text{ft}^2 \]
Now you can divide the remaining 192 ft² between the nonfiction and novels sections. If you want to divide them equally, each would get:
\[ \text{Area for each remaining section} = \frac{192 , \text{ft}^2}{2} = 96 , \text{ft}^2 \]
You can then choose dimensions (width and length) for the nonfiction and novels sections based on their areas.
For example, if both sections have a width of 12 ft as well, each will be:
\[ \text{Length} = \frac{96 , \text{ft}^2}{12 , \text{ft}} = 8 , \text{ft} \]
Thus the dimensions for each section could be configured as follows:
- Stationary Section: 12 ft (width) × 8 ft (length)
- Nonfiction Section: 12 ft (width) × 8 ft (length)
- Novels Section: 12 ft (width) × 8 ft (length)
This ensures that all three sections together form the total area of the bookstore.
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