Question

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 ÷

Make sure no one can find this

Make sure it's right

Answer 1

To solve this problem, we start by confirming the scale factor relating the two drawings.

Maya's original scale drawing has a scale factor of 1:2. She wants to convert this to a scale factor of 1:6. The relationship between these two scale factors is determined by dividing the original scale factor by the new scale factor:

\[
\text{Scale Factor Relation} = \frac{1/2}{1/6} = \frac{1/2 \times 6/1} = \frac{6}{2} = 3
\]

### Scale Factor Relation
The scale factor relating the two scale drawings to each other is **3**.

### Finding Dimensions of the Smaller Scale Drawing
Next, we need to find the dimensions of the smaller scale drawing using the scale factor of 1:6.

Maya's first scale drawing dimensions are:
- Length: 12 inches (top and bottom)
- Width: 6 inches (left and right)

To find the dimensions of the smaller drawing (1:6), we multiply the dimensions of the original scale drawing (1:2) by the scale factor of 1:6, which means we need to adjust the dimensions based on their original scale.

To get the actual dimensions:
1. For the original length (12 inches in a 1:2 drawing), the actual length would be:
\[
\text{Actual Length} = 12 \, \text{inches} \times 2 = 24 \, \text{inches}
\]
For the smaller scale (1:6), we now divide this length by 6:
\[
\text{Smaller Length} = \frac{24}{6} = 4 \, \text{inches}
\]

2. For the original width (6 inches in a 1:2 drawing), the actual width would be:
\[
\text{Actual Width} = 6 \, \text{inches} \times 2 = 12 \, \text{inches}
\]
Again, divide this width by 6 for the smaller scale:
\[
\text{Smaller Width} = \frac{12}{6} = 2 \, \text{inches}
\]

### Final Answers for Blanks:
1. The length of the new rectangle is **4** inches.
2. The width of the new rectangle is **2** inches.

Thus, the complete statement could be:

"The width of the new rectangle is **4** inches and the height is **2** inches."

Also, using your provided options for blank 2, the operation to find new dimensions from the original would be **÷**, so the complete sentence would be:

"The window of the new rectangle is **blank 1** **blank 2** **blank 3** = **blank 4**" with the relevant numbers and operations filled in.

Finally:
- Blank 1: 24 (actual length)
- Blank 2: ÷
- Blank 3: 6
- Blank 4: 4 (new length)
- Blank 5: 2 (width)

So the sentences considering that context could be structured as needed.