To find the scale factor that relates the two scale drawings to each other, we can compare the original scale factor of \(1:2\) to the new scale factor of \(1:6\).
The relation can be expressed as: \[ \text{Scale factor between drawings} = \frac{1/2}{1/6} = \frac{1}{2} \times \frac{6}{1} = 3 \] This means the first drawing is \(3\) times larger than the second drawing.
Now, we can find the lengths for the smaller drawing (1:6 scale).
The original dimensions for the \(1:2\) scale drawing are:
- Length: \(12\) inches
- Width: \(6\) inches
To convert these dimensions to the \(1:6\) scale, we divide each dimension by \(3\) (the scale factor we just calculated).
For the length of the smaller scale drawing: \[ \text{Length} = \frac{12 \text{ inches}}{3} = 4 \text{ inches} \]
For the width of the smaller scale drawing: \[ \text{Width} = \frac{6 \text{ inches}}{3} = 2 \text{ inches} \]
Thus, the filled in statements in your structure would look like this:
The widow (window) of the new rectangle is \(12 \text{ inches} ; \text{(length)} , \text{blank 1} , 6 \text{ inches} ; \text{(width)} ; \text{blank 2} = 4 \text{ inches} \) (new length \(blank 4\)).
The width of the new rectangle is \(2 \text{ inches} \) (blank 5).
Therefore:
- Blank 1 = ÷ (to denote the relationship).
- Blank 2 = = (to denote the equality).
- Blank 4 = 4 inches (the calculated new length).
- Blank 5 = 2 inches (the calculated new width).
So, to summarize:
- The scale factor relating the two drawings is \(3\).
- The length of the new rectangle is \(4\) inches.
- The width of the new rectangle is \(2\) inches.