1. **Problem statement:** (a) Find the distance in cm between two stadiums on Map B whose scale is 1:5000 given the distance on Map A (scale 1:2000) is 12.5 cm. (b) Given the area of the house on Map B (scale 1:5000) is 15 cm², find the area of the house on Map A (scale 1:2000). 2. **Understanding the scales and distances:** The scale 1:2000 means 1 cm on Map A represents 2000 cm in real life. The scale 1:5000 means 1 cm on Map B represents 5000 cm in real life. 3. **Find the actual real-life distance between the stadiums:** $$\text{Actual distance} = 12.5 \times 2000 = 25000 \text{ cm}$$ 4. **Find the distance between the stadiums on Map B:** Let distance on Map B be $x$ cm. Since 1 cm on Map B = 5000 cm real-life, $$x \times 5000 = 25000$$ $$x = \frac{25000}{5000} = 5\text{ cm}$$ 5. **Find the area scale factor:** Area scales with the square of the linear scale. Scale ratio of Map A to Map B = $\frac{1}{2000} \div \frac{1}{5000} = \frac{5000}{2000} = 2.5$ So, $$\text{Area scale factor} = (2.5)^2 = 6.25$$ 6. **Find the area of the house on Map A:** $$\text{Area on Map A} = 15 \times 6.25 = 93.75 \text{ cm}^2$$ **Final answers:** (a) Distance on Map B = 5 cm (b) Area on Map A = 93.75 cm²