The area of mirror A is 100/49 times greater than the area of mirror B, determined by converting side lengths to improper fractions, calculating areas, and simplifying the resulting fraction.
Calculate the area of each mirror using the formula area = side length x side length and then divide the area of mirror A by the area of mirror B. Here are the steps:
Convert the side lengths of the mirrors from mixed numbers to improper fractions. For example, 2 1/2 = 5/2 and 1 3/4 = 7/4.
Calculate the area of mirror A by multiplying 5/2 by 5/2. This gives 25/4 square feet.
Calculate the area of mirror B by multiplying 7/4 by 7/4. This gives 49/16 square feet.
Divide the area of mirror A by the area of mirror B by multiplying 25/4 by the reciprocal of 49/16. This gives 100/49.
Simplify the fraction by dividing both the numerator and the denominator by the greatest common factor, which is 1. This gives 100/49 as the final answer.
Therefore, the area of mirror A is 100/49 times greater than the area of mirror B.