Answer :
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.
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.