Let's work through this problem step-by-step to find the remaining area after cutting out a smaller square from a larger square.
1. Determine the area of the larger square:
- The side length of the larger square is 24 feet.
- Area of a square is calculated as: [tex]\[ \text{Area} = \text{side}^2 \][/tex]
- So, the area of the larger square is: [tex]\[ 24 \times 24 = 576 \text{ square feet} \][/tex]
2. Determine the area of the smaller square:
- The side length of the smaller square is 17 feet.
- Using the same formula for the area of a square: [tex]\[ \text{Area} = \text{side}^2 \][/tex]
- So, the area of the smaller square is: [tex]\[ 17 \times 17 = 289 \text{ square feet} \][/tex]
3. Calculate the remaining area after cutting out the smaller square:
- To find the remaining area, subtract the area of the smaller square from the area of the larger square.
- [tex]\[ \text{Remaining Area} = \text{Area of the larger square} - \text{Area of the smaller square} \][/tex]
- So the remaining area is: [tex]\[ 576 - 289 = 287 \text{ square feet} \][/tex]
Thus, the remaining board after cutting out the smaller square is 287 square feet. This does not match any of the provided options (200 ft², 300 ft², 400 ft², 600 ft²), so there might be an error or misunderstanding in the problem setup or the options provided. Nevertheless, based on our calculations, the remaining area is indeed 287 square feet.
