1. **State the problem:** We have two similar trapezoids DEFG (original) and JKLM (new). The top base of DEFG is 40 m, and the corresponding top base of JKLM is 8 m. The left side of DEFG is 30 m, and the corresponding left side of JKLM is $x$ m. We need to find the scale factor from the original to the new trapezoid and then find the value of $x$. 2. **Formula and rules:** For similar figures, corresponding sides are proportional. The scale factor $k$ is the ratio of any pair of corresponding sides: $$k = \frac{\text{side in new figure}}{\text{corresponding side in original figure}}$$ 3. **Find the scale factor:** Using the top bases, $$k = \frac{8}{40} = \frac{8}{40}$$ Simplify the fraction: $$k = \frac{\cancel{8}}{\cancel{40}} = \frac{1}{5}$$ So, the scale factor is $\frac{1}{5}$. 4. **Find $x$:** Since the trapezoids are similar, the left sides are proportional: $$\frac{x}{30} = \frac{1}{5}$$ Multiply both sides by 30: $$x = 30 \times \frac{1}{5}$$ Simplify: $$x = \frac{30}{\cancel{5}} \times \frac{1}{\cancel{1}} = 6$$ 5. **Final answer:** The scale factor is $\frac{1}{5}$ and the value of $x$ is 6 meters.