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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

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

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

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

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

To identify the ratios for the bases and heights within the similar rectangles QRST and ABCD, we can compare their corresponding lengths and widths:

  1. For the length (bases):

    • Length of QRST (Q T or R S) = 21
    • Length of ABCD (A B or C D) = 28
    • Ratio of lengths = \( \frac{21}{28} \)

  2. For the width (heights):

    • Width of QRST (Q R or S T) = 12
    • Width of ABCD (A D or B C) = 16
    • Ratio of widths = \( \frac{12}{16} \)

So, we need to verify that the ratios of the lengths and widths are equal:

  • The ratio of the bases: \( \frac{21}{28} = \frac{3}{4} \)
  • The ratio of the heights: \( \frac{12}{16} = \frac{3}{4} \)

Both ratios simplify to \( \frac{3}{4} \), confirming that the rectangles are similar.

Given this analysis, the correct answer is:

Start Fraction 21 over 28 End Fraction equals Start Fraction 12 over 16 End Fraction