1. **State the problem:** We have two similar rectangles ABCD and WXYZ. We know the length of ABCD is 35 inches and the length of WXYZ is 5 inches. The width of WXYZ is 3 inches, and we want to find the width $x$ of ABCD and the scale factor from ABCD to WXYZ. 2. **Formula and rules:** For similar figures, corresponding sides are proportional. The scale factor $k$ from the original to the new shape is given by: $$k = \frac{\text{new side}}{\text{original side}}$$ 3. **Find the scale factor using the lengths:** $$k = \frac{5}{35} = \frac{1}{7}$$ 4. **Use the scale factor to find $x$:** Since the widths correspond, $$k = \frac{3}{x}$$ 5. **Solve for $x$:** $$\frac{1}{7} = \frac{3}{x}$$ Multiply both sides by $x$: $$x \times \frac{1}{7} = 3$$ $$\frac{x}{7} = 3$$ Intermediate step showing cancellation: $$\frac{\cancel{x}}{7} = 3$$ Multiply both sides by 7: $$x = 3 \times 7$$ $$x = 21$$ **Final answer:** The scale factor is $\frac{1}{7}$ and the value of $x$ is 21 inches.