A rectangle is reduced by a scale factor of one-fourth. The larger rectangle has a length of 16 and a width of 12, while the smaller rectangle has a length of 4 and a width of 3. Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options. a. 4 / 16 b. (4 / 16) squared c. 12 / 192 d. (4^2) / (16^2) e. 3 / (12^2)

To determine the ratio of the area of the smaller rectangle to the area of the larger rectangle, we first need to calculate the areas of the two rectangles. The area of a rectangle is found by multiplying the length by the width.

For the larger rectangle: Length (L) = 16 Width (W) = 12 Area (A) = L × W = 16 × 12 = 192 square units

For the smaller rectangle: Length (l) = 4 Width (w) = 3 Area (a) = l × w = 4 × 3 = 12 square units

Now, we will find the ratio of the area of the smaller rectangle to the area of the larger rectangle:

Ratio = Area of smaller rectangle / Area of larger rectangle = 12 / 192

This fraction can be simplified by dividing both the numerator and the denominator by 12:

12 ÷ 12 / 192 ÷ 12 = 1 / 16

Now let's look at the provided options:

a. 4 / 16 - This option represents the ratio of the lengths, not the areas. b. (4 / 16) squared - This option is the correct one because the area of similar shapes is proportional to the square of the scale factor, which in this case is 1/4. c. 12 / 192 - This is the simplified ratio of the area of the smaller rectangle to the area of the larger rectangle, which is 1 / 16 in the simplified form. d. (4^2) / (16^2) - This option correctly uses the squared scale factor for the area ratio, making it another correct choice. e. 3 / (12^2) - This option does not represent a ratio that has been squared and is not relevant to the areas of the rectangles.

Therefore, the correct options that show the ratio of the area of the smaller rectangle to the area of the larger rectangle are (b), (c), and (d).