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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

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

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

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
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Answer 1

To compare the ratios of the lengths and widths of the similar rectangles QRST and ABCD, we can find the ratios of their corresponding sides:

1. For the lengths:

   • Length of rectangle QRST (QT, RS): 21
   • Length of rectangle ABCD (AB, CD): 28
   • Ratio of lengths: \( \frac{21}{28} \)

2. For the widths:

   • Width of rectangle QRST (QR, ST): 12
   • Width of rectangle ABCD (AD, BC): 16
   • Ratio of widths: \( \frac{12}{16} \)

Now, we simplify both ratios:

• The ratio of lengths: \( \frac{21}{28} = \frac{3}{4} \)

• The ratio of widths: \( \frac{12}{16} = \frac{3}{4} \)

Thus, both ratios are equal, and the correct response that represents this equality is:

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

So the correct answer is: Start Fraction 21 over 28 End Fraction equals Start Fraction 12 over 16 End Fraction. (This matches the second option given.)

Answer 2

Are you sure?

Answer 3

Let's clearly analyze the ratios again step by step:

For rectangles QRST and ABCD, the dimensions are as follows:

For rectangle QRST:

• Length (QT and RS) = 21
• Width (QR and ST) = 12

For rectangle ABCD:

• Length (AB and CD) = 28
• Width (AD and BC) = 16

Now, we can express these dimensions as ratios:

1. Ratio of lengths:

   • \( \frac{21}{28} \)

2. Ratio of widths:

   • \( \frac{12}{16} \)

Now let's simplify both ratios:

• For lengths:

  • \( \frac{21}{28} = \frac{3}{4} \) (divide both by 7)

• For widths:

  • \( \frac{12}{16} = \frac{3}{4} \) (divide both by 4)

The ratios are indeed equal: \( \frac{21}{28} = \frac{12}{16} = \frac{3}{4} \).

Therefore, the correct representation of the ratios is:

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

This corresponds to option (2) from your provided list:

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

So yes, I confirm that this is correct! Thank you for your patience.