Rectangle QRST is similar to rectangle ABCD. Identify the ratios for the bases and heights within the similar rectangles.

To determine which ratios correspond to the similar rectangles QRST and ABCD, we need to identify the ratios of the bases and heights.

For rectangles that are similar, the ratio of corresponding sides (bases and heights) are equal.

Let's analyze the given options:

1. 2112 = 1628

   • This can be expressed as:
   • \( \frac{21}{12} = \frac{16}{28} \)
   • Simplifying both fractions:
     • \( \frac{21}{12} ; \text{(cannot be simplified)} \)
     • \( \frac{16}{28} \) simplifies to \( \frac{4}{7} \) (dividing numerator and denominator by 4)
     • Ratios are not equal.

2. 2112 = 2816

   • This can be expressed as:
   • \( \frac{21}{12} = \frac{28}{16} \)
   • Simplifying both fractions:
     • \( \frac{21}{12} ; \text{(cannot be simplified)} \)
     • \( \frac{28}{16} \) simplifies to \( \frac{7}{4} \) (dividing numerator and denominator by 4)
     • Ratios are not equal.

3. 2821 = 1612

   • This can be expressed as:
   • \( \frac{28}{21} = \frac{16}{12} \)
   • Simplifying both fractions:
     • \( \frac{28}{21} = \frac{4}{3} \) (dividing numerator and denominator by 7)
     • \( \frac{16}{12} = \frac{4}{3} \) (dividing numerator and denominator by 4)
     • Ratios are equal.

4. 2128 = 1216

   • This can be expressed as:
   • \( \frac{21}{28} = \frac{12}{16} \)
   • Simplifying both fractions:
     • \( \frac{21}{28} = \frac{3}{4} \) (dividing numerator and denominator by 7)
     • \( \frac{12}{16} = \frac{3}{4} \) (dividing numerator and denominator by 4)
     • Ratios are equal.

Thus, the options 2821 = 1612 and 2128 = 1216 provide equal ratios for the bases and heights. If you need to select a single answer, you can choose either of those as matching ratios for the similar rectangles.