27. What is the area, in square units, of the image of PQRS?
Answer: B
The area of the image of square PQRS is 25 square units.
The area of a square is calculated by squaring the length of one of its sides. Since the side length of square PQRS is 5 units, the area is 5 x 5, which equals 25 square units.
A) 20
This option is incorrect because the area of the square is calculated by squaring the length of its side, which is 5 units. Thus, 5 x 5 equals 25, not 20.
B) 25
This option is correct as it accurately represents the area of square PQRS. The area is calculated as the side length squared (5 x 5), resulting in 25 square units.
C) 40
This option is incorrect because it suggests an area that exceeds the calculated area of the square. The area cannot be 40 since the maximum area based on the side length of 5 units is 25 square units.
D) 50
This option is incorrect as it implies a much larger area than what is possible for square PQRS. The area calculations based on the side length of 5 units demonstrate that the area cannot exceed 25 square units.
E) 100
This option is incorrect as it suggests a square area that is not possible given the side length of 5 units. The area of a square with a side length of 5 units is constrained to 25 square units.
Conclusion
The correct answer is 25 square units, as it directly results from squaring the side length of the square PQRS. All other options fail to represent the calculated area based on the provided dimensions, confirming that option B is the only accurate choice.