1. **State the problem:** We have two similar trapezoids DEFG (original) and JKLM (new). We know the height of DEFG is 48 m and the height of JKLM is 12 m. The top base of JKLM is 16 m, and the top base of DEFG is $x$ m. We need to find the scale factor from the original to the new trapezoid and then find $x$. 2. **Formula and rules:** For similar figures, corresponding lengths are proportional. The scale factor $k$ is the ratio of any pair of corresponding lengths. Here, the heights correspond, so: $$k = \frac{\text{new height}}{\text{original height}} = \frac{12}{48}$$ 3. **Calculate the scale factor:** $$k = \frac{12}{48} = \frac{\cancel{12}^1}{\cancel{48}^4} = \frac{1}{4}$$ 4. **Use the scale factor to find $x$:** Since the top bases correspond, $$k = \frac{\text{new top base}}{\text{original top base}} = \frac{16}{x}$$ 5. **Solve for $x$:** $$\frac{1}{4} = \frac{16}{x}$$ Multiply both sides by $x$: $$x \times \frac{1}{4} = 16$$ $$\frac{x}{4} = 16$$ Multiply both sides by 4: $$x = 16 \times 4 = 64$$ 6. **Final answer:** - Scale factor is $\frac{1}{4}$. - The value of $x$ is 64 meters.