Final answer:
To find the area of the rectangle with the given dimensions, one would need to multiply (3 √5 - 8 √3) by 12.52. The area can't be precisely calculated without the exact values for √5 and √3. However, the result should be expressed in square units to the proper number of significant figures.
Step-by-step explanation:
The area of a rectangle is calculated by multiplying its length by its width. The question gives us the dimensions of the rectangle in a slightly complex form, one of which involves a radical expression. However, before we can calculate the area, we need to simplify the expression for the rectangle's length, 3 √5 - 4 √12. First, we must simplify √12, which is equivalent to 2√3. As such, the expression simplifies to 3 √5 - 8 √3. Since we cannot directly simplify this expression further without knowing the values of √5 and √3 and since they are not like terms, they cannot be combined.
However, the given conditions seem to suggest the width is 1.25 cm, reported to three significant figures. Still, based on the original question, we'll assume the measured width to be 12.52, which is not necessarily related to the width mentioned in the supplied context. To find the area (A), we use the formula A = length × width. Without the exact values for the radicals, we would multiply the entire expression for the length by 12.52 to find the area in the appropriate square units.