Final answer:
When the sides of a rectangle are doubled, the new area will be four times the original area. Therefore, if the original area is 12 cm², the new area will be 48 cm².
Step-by-step explanation:
The student has asked what the new area of a rectangle will be if each of its sides is doubled in length, given that the original area is 12 cm2. Doubling the length of each side of a rectangle results in a new rectangle whose dimensions are twice as large as the original. Importantly, when we double the lengths of both sides, the area of the rectangle becomes four times larger since area is proportional to the square of the scale factor. In this case, the scale factor for the lengths is 2, so the scale factor for the area is 22 or 4.
Original area of the rectangle: 12 cm2
New area of the rectangle: 12 cm2 × 4 = 48 cm2