Final answer:
The length of the crease DE in the paper triangle is 4.8 cm, which is determined by using the ratio of the areas of the triangles ABC and DE, and knowing that the area of the projecting triangle is 16% that of triangle ABC.
Step-by-step explanation:
To find the length of the crease DE, we start by understanding that DE is parallel to the base AB, and thus creates a similar smaller triangle within triangle ABC. Since the area of the projecting triangle is 16% that of triangle ABC, we can set up a ratio to solve for the unknown length of DE.
The area of a triangle is calculated using the formula ½ × base × height. If the crease DE is x cm from the base AB, then the areas of the similar triangles are proportional, and the ratio of their bases is the square root of the ratio of their areas. In this case, the ratio of the areas is 16:100 or 4:25 after reduction, which simplifies to 2:5 when we take the square root for the ratio of the bases (since the height remains the same for both triangles).
Thus, if AB = 12 cm, we have AB/DE = 5/2, and DE = (2/5) × 12 cm = 4.8 cm. Therefore, the correct answer is (D).