Question

Use the image to answer the question.

An illustration shows two similar rectangles.
On rectangle Q R S T, the length of sides Q T and R S measures 21. The width of sides Q R and S T measures 12. Right angle symbols are shown at all four vertices. On rectangle A B C D, the length of sides A B and C D measures 28. The width of sides A D and B C measures 16. Right angle symbols are shown at all four vertices.

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

(1 point)
Responses

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

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

2128=1216
Start Fraction 21 over 28 End Fraction equals Start Fraction 12 over 16 End Fraction

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

Answer 1

To determine the ratios of the bases and heights within the similar rectangles QRST and ABCD, we can analyze the dimensions given:

- For rectangle QRST:
- Length (base) = 21
- Width (height) = 12

- For rectangle ABCD:
- Length (base) = 28
- Width (height) = 16

We can set up the ratios as follows:

**Ratios for lengths (bases):**
\[
\frac{21}{28}
\]

**Ratios for widths (heights):**
\[
\frac{12}{16}
\]

Next, we will simplify both ratios:

1. **Simplifying the length ratio:**
\[
\frac{21}{28} = \frac{3}{4}
\]

2. **Simplifying the width ratio:**
\[
\frac{12}{16} = \frac{3}{4}
\]

Since these ratios are equal, we can express the final ratios of the bases and heights as follows:

**Final Ratio:**
\[
\frac{21}{12} = \frac{28}{16}
\]

Matching this with the provided responses, we have:

- \( \frac{21}{12} = \frac{28}{16} \)

Therefore, the correct response is:

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