42. A rectangle has a width of 3 centimeters. If the length is increased by 6 centimeters, by how much will the area, in square centimeters, increase?
Answer: D
The area will increase by 18 square centimeters.
When the length of the rectangle is increased by 6 centimeters, the area increases by 18 square centimeters, calculated by finding the difference in area before and after the length increase.
A) 3
This option is incorrect because an increase of 3 square centimeters does not reflect the change in area resulting from a 6-centimeter increase in length. The area increase must account for both the original width and the additional length.
B) 6
This option is also incorrect as it does not consider the total area affected by the increase in length. Simply stating an increase of 6 square centimeters fails to capture the effect of the 3-centimeter width multiplied by the 6-centimeter length increase.
C) 12
While this option suggests a significant increase, it is not accurate. An increase of 12 square centimeters does not account for the complete calculation of the area change, which requires multiplying the full width by the increase in length.
D) 18
This option is correct because the area increase is calculated by taking the width (3 cm) and multiplying it by the increase in length (6 cm), resulting in an increase of 18 square centimeters (3 cm * 6 cm = 18 cm²).
Conclusion
The correct answer is 18 square centimeters, as it accurately reflects the increase in area due to the length adjustment. All other options fail to account for the necessary multiplication of the original width by the change in length, leading to an underestimation of the area increase.