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Maya created several possible ways to rearrange her hamster's cage to give the hamster more room to run around. Her drawings were made with a scale factor of 1:2, but she wants to change the scale factor to 1:6 so she can compare them more easily.

The diagram shows the lengths of the sides of her first scale drawing and the scale factors relating both drawings to the actual cage.

Identify the scale factor that relates the two scale drawings to each other. Then, find the length and width of the smaller scale drawing.

Scale Factor of 1:2 is
12 In top and bottom
6 left and right

Scale factor 1:6 unknown

The new scale factor is 1/2 ÷ 1/6 = 3

The widow the new rectangle is *blank 1* *blank 2* *blank 3* = *blank 4*
The width of the new rectangle is *blank 5* inches

Options for blank 2

A -
B +
C ●
D ÷

Options for blank 3
A 3/1
B 3
C 1/3

Make sure no one can find this

Make sure it's right

1 answer

To find the scale factor that relates the two scale drawings to each other, you can indeed divide the two scale factors:

  1. The original scale factor is \( \frac{1}{2} \).
  2. The new scale factor is \( \frac{1}{6} \).

The scale factor relating the two drawings is calculated as follows:

\[ \frac{1/2}{1/6} = \frac{1}{2} \times \frac{6}{1} = 3 \]

So the scale factor relating the two drawings is 3.

Now, to find the dimensions of the smaller scale drawing (the one with a scale factor of \( 1:6 \)), we need to scale down the dimensions from the \( 1:2 \) drawing:

  • Top and Bottom length in the \( 1:2 \) drawing: 12 inches
  • Left and Right width in the \( 1:2 \) drawing: 6 inches

For the \( 1:6 \) scale:

  1. Length (12 inches from \( 1:2 \)): \[ \text{Length} = \frac{12 \text{ inches}}{3} = 4 \text{ inches} \]

  2. Width (6 inches from \( 1:2 \)): \[ \text{Width} = \frac{6 \text{ inches}}{3} = 2 \text{ inches} \]

So, the dimensions of the smaller scale drawing are:

  • Length: 4 inches
  • Width: 2 inches

Now, filling in the blanks:

  • The width of the new rectangle is 4 inches
  • The length of the new rectangle is 2 inches
  • The operation used to find the scale factor is ÷, so the answer for blank 2 is B.

Final Answer:

  1. blank 1: 3
  2. blank 2: + (the operation should be ÷, so please correct this)
  3. blank 3: 3
  4. blank 4: 4
  5. blank 5: 2 inches

If it needs to align directly with your given format, fill in:

  • The length of the new rectangle is 4 inches.
  • The width of the new rectangle is 2 inches.

Thus the correct answer choices for blanks are:

  • blank 1: 3
  • blank 2: ÷ (Note: Please correct to reflect the operations on the scale factor)
  • blank 3: 3.

Let me know if you need any additional information!