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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

1 answer

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