1. **State the problem:** We have two maps showing the same forest. The first map has a scale of 1 : 20 000 and the forest area is 50 cm². The second map shows the forest area as 8 cm². We need to find the scale of the second map. 2. **Recall the formula for area scale:** The area on the map is proportional to the square of the linear scale. If the linear scale is $S$, then the area scale factor is $S^2$. 3. **Set up the ratio of areas:** Let the scale of the second map be $1 : x$. Then the ratio of areas is $$\frac{8}{50} = \left(\frac{1/x}{1/20000}\right)^2 = \left(\frac{20000}{x}\right)^2$$ 4. **Solve for $x$:** $$\frac{8}{50} = \frac{20000^2}{x^2}$$ Multiply both sides by $x^2$: $$x^2 \times \frac{8}{50} = 20000^2$$ Divide both sides by $\frac{8}{50}$: $$x^2 = \frac{20000^2}{\frac{8}{50}} = 20000^2 \times \frac{50}{8}$$ 5. **Calculate $x$:** $$x = \sqrt{20000^2 \times \frac{50}{8}} = 20000 \times \sqrt{\frac{50}{8}}$$ Simplify inside the square root: $$\sqrt{\frac{50}{8}} = \sqrt{6.25} = 2.5$$ So, $$x = 20000 \times 2.5 = 50000$$ 6. **Final answer:** The scale of the second map is $1 : 50000$. This means the second map is less detailed, showing the forest smaller relative to the real size.