Question
The area of the red square is 16 . The area of the yellow square is 25 .
What is the area of the green square?
Responses
A 3 3 ft 2
B 9 9 ft 2
C 81 81 ft 2
D 128 128 ft 2
E 256
What is the area of the green square?
Responses
A 3 3 ft 2
B 9 9 ft 2
C 81 81 ft 2
D 128 128 ft 2
E 256
Answers
GPT-4o mini
To solve for the area of the green square, we need to first understand the relationship between the areas of the red and yellow squares.
We know the following:
- The area of the red square is 16, which means that the side length of the red square is \( \sqrt{16} = 4 \) feet.
- The area of the yellow square is 25, which means that the side length of the yellow square is \( \sqrt{25} = 5 \) feet.
Since the problem does not specify the position or connection between the squares, we can assume a possible spatial arrangement. A common assumption in similar problems is that the green square is related to the other two squares through some geometric property, such as being the square of the sum of the sides or some other combination.
A reasonable hypothesis given the information is that the green square might be the square formed by the addition of the two smaller squares (i.e., placing them edge-to-edge or corner-to-corner).
Thus, the side length of the green square could be \( 4 + 5 = 9 \) feet.
Thus, the area of the green square would be:
\[
\text{Area} = \text{side length}^2 = 9^2 = 81 \text{ ft}^2
\]
Therefore, the area of the green square is \( 81 \text{ ft}^2 \).
The correct response is:
**C 81 ft².**
We know the following:
- The area of the red square is 16, which means that the side length of the red square is \( \sqrt{16} = 4 \) feet.
- The area of the yellow square is 25, which means that the side length of the yellow square is \( \sqrt{25} = 5 \) feet.
Since the problem does not specify the position or connection between the squares, we can assume a possible spatial arrangement. A common assumption in similar problems is that the green square is related to the other two squares through some geometric property, such as being the square of the sum of the sides or some other combination.
A reasonable hypothesis given the information is that the green square might be the square formed by the addition of the two smaller squares (i.e., placing them edge-to-edge or corner-to-corner).
Thus, the side length of the green square could be \( 4 + 5 = 9 \) feet.
Thus, the area of the green square would be:
\[
\text{Area} = \text{side length}^2 = 9^2 = 81 \text{ ft}^2
\]
Therefore, the area of the green square is \( 81 \text{ ft}^2 \).
The correct response is:
**C 81 ft².**