Question
12 in on the top and bottom 6 in on left and right
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.
The new Scale Factor is 1/2 - 1/6 = 1/3
The width of the new rectangular is W ÷ 1/3 = W/3
The width of the new rectangle is W/3 inches.
The height of the new rectangle *blank 1* ● *blank 2* = *blank 3*
The height of the new rectangle is *blank 4* inches
Options for blank 2
A 3
B 3/1
C 1/3
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.
The new Scale Factor is 1/2 - 1/6 = 1/3
The width of the new rectangular is W ÷ 1/3 = W/3
The width of the new rectangle is W/3 inches.
The height of the new rectangle *blank 1* ● *blank 2* = *blank 3*
The height of the new rectangle is *blank 4* inches
Options for blank 2
A 3
B 3/1
C 1/3
Answers
GPT-4o mini
To find the relationships and answer the blanks, let's clarify the steps involved in identifying the scale factor and dimensions of the smaller drawing.
1. **Identifying the Scale Factor**:
- The original scale factor is 1:2.
- The new scale factor is 1:6.
- To find the scale factor relating the two scale drawings (from 1:2 to 1:6), we can calculate the ratio:
- Scale factor from the first drawing to the second drawing = (1/2) ÷ (1/6) = (1/2) * (6/1) = 6/2 = 3.
- Therefore, the scale factor relating the two drawings to each other is **3**.
2. **Finding the Length and Width of the Smaller Scale Drawing**:
- Given dimensions for the first scale drawing:
- Height = 12 inches
- Width = 6 inches
- To find the dimensions of the smaller scale drawing (with a scale factor of 1:6), we will use the new scale factor:
- For the height:
- Original height: 12 inches
- New height = (12 inches) * (1/6) = 2 inches
- For the width:
- Original width: 6 inches
- New width = (6 inches) * (1/6) = 1 inch
3. **Filling in the Blanks**:
- The height of the new rectangle is established as:
- Height of the new rectangle = **2 inches**.
- The expression for height:
- Height of the new rectangle **2 * 3 = 6** (noting that the multiplication of height with 3 leads relates to the larger drawing back).
- This translates to:
- **Blank 1** → 2
- **Blank 2** → 3
- **Blank 3** → 6 (implying a relationship with dimensions based on prior scaling)
- **Blank 4** → 2 inches
Thus, your completed statement will look like:
- The height of the new rectangle *2* ● *3* = *6*
- The height of the new rectangle is *2* inches.
For the options provided:
- **Blank 2** corresponds to option A (3).
1. **Identifying the Scale Factor**:
- The original scale factor is 1:2.
- The new scale factor is 1:6.
- To find the scale factor relating the two scale drawings (from 1:2 to 1:6), we can calculate the ratio:
- Scale factor from the first drawing to the second drawing = (1/2) ÷ (1/6) = (1/2) * (6/1) = 6/2 = 3.
- Therefore, the scale factor relating the two drawings to each other is **3**.
2. **Finding the Length and Width of the Smaller Scale Drawing**:
- Given dimensions for the first scale drawing:
- Height = 12 inches
- Width = 6 inches
- To find the dimensions of the smaller scale drawing (with a scale factor of 1:6), we will use the new scale factor:
- For the height:
- Original height: 12 inches
- New height = (12 inches) * (1/6) = 2 inches
- For the width:
- Original width: 6 inches
- New width = (6 inches) * (1/6) = 1 inch
3. **Filling in the Blanks**:
- The height of the new rectangle is established as:
- Height of the new rectangle = **2 inches**.
- The expression for height:
- Height of the new rectangle **2 * 3 = 6** (noting that the multiplication of height with 3 leads relates to the larger drawing back).
- This translates to:
- **Blank 1** → 2
- **Blank 2** → 3
- **Blank 3** → 6 (implying a relationship with dimensions based on prior scaling)
- **Blank 4** → 2 inches
Thus, your completed statement will look like:
- The height of the new rectangle *2* ● *3* = *6*
- The height of the new rectangle is *2* inches.
For the options provided:
- **Blank 2** corresponds to option A (3).