1. **Problem Statement:** We need to find the scale factor to reproduce a blueprint so that its area becomes 45 square inches and it fits on a standard sheet of paper. 2. **Understanding the problem:** When scaling a two-dimensional figure, the area scales by the square of the scale factor. If the original area is $A_0$ and the scale factor is $k$, then the new area $A$ is given by: $$A = k^2 \times A_0$$ 3. **Given:** - New area $A = 45$ square inches - Original area $A_0$ is not explicitly given, so we assume it is known or we want to express $k$ in terms of $A_0$. 4. **Find the scale factor $k$:** Rearranging the formula: $$k = \sqrt{\frac{A}{A_0}}$$ 5. **Interpretation:** - If the original blueprint area $A_0$ is known, plug it in to find $k$. - The scale factor $k$ is the ratio of the new length to the original length. 6. **Converting units:** - If the scale factor is in inches to feet, recall that 1 foot = 12 inches. - So, if $k$ is the scale factor in inches, then in feet it is $\frac{k}{12}$. 7. **Summary:** - To reproduce the blueprint with area 45 square inches, scale lengths by $k = \sqrt{\frac{45}{A_0}}$. - Then convert $k$ inches to feet by dividing by 12. **Final answer:** $$\text{Scale factor} = \sqrt{\frac{45}{A_0}} \quad \text{(inches)} = \frac{1}{12} \sqrt{\frac{45}{A_0}} \quad \text{(feet)}$$