Question
a bedroom floor is a rectangle with an area of 126 square feet. there are three identical non-overlapping square rugs on the floor, with side lengths of 4 feet. what area of the floor, in square feet, is not covered by rugs?
48
78
110
114
48
78
110
114
Answers
GPT-4o mini
To find the area of the bedroom floor that is not covered by the rugs, we need to first calculate the area covered by the rugs and then subtract that from the total area of the floor.
1. **Total area of the bedroom floor**: 126 square feet.
2. **Area of one square rug**:
\[
\text{Area} = \text{side length}^2 = 4 \text{ ft} \times 4 \text{ ft} = 16 \text{ square feet}
\]
3. **Area covered by three rugs**:
\[
\text{Total area of rugs} = 3 \times \text{Area of one rug} = 3 \times 16 \text{ square feet} = 48 \text{ square feet}
\]
4. **Calculating the area of the floor that is not covered by the rugs**:
\[
\text{Area not covered} = \text{Total area of the floor} - \text{Total area of rugs} = 126 \text{ square feet} - 48 \text{ square feet} = 78 \text{ square feet}
\]
Therefore, the area of the floor that is not covered by rugs is \(\boxed{78}\) square feet.
1. **Total area of the bedroom floor**: 126 square feet.
2. **Area of one square rug**:
\[
\text{Area} = \text{side length}^2 = 4 \text{ ft} \times 4 \text{ ft} = 16 \text{ square feet}
\]
3. **Area covered by three rugs**:
\[
\text{Total area of rugs} = 3 \times \text{Area of one rug} = 3 \times 16 \text{ square feet} = 48 \text{ square feet}
\]
4. **Calculating the area of the floor that is not covered by the rugs**:
\[
\text{Area not covered} = \text{Total area of the floor} - \text{Total area of rugs} = 126 \text{ square feet} - 48 \text{ square feet} = 78 \text{ square feet}
\]
Therefore, the area of the floor that is not covered by rugs is \(\boxed{78}\) square feet.