Question

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

(1 point)
Responses

2112=1628
Start Fraction 21 over 12 End Fraction equals Start Fraction 16 over 28 End Fraction

2112=2816
Start Fraction 21 over 12 End Fraction equals Start Fraction 28 over 16 End Fraction

2821=1612
Start Fraction 28 over 21 End Fraction equals Start Fraction 16 over 12 End Fraction

2128=1216

Answer 1

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.