Kim wants to draw a scale diagram of a conservation park which is 10 km long and 6 km wide. She needs the diagram to fit on an A3 sheet of paper which is 42 cm long and 29.7 cm wide. Which of these scales would be most appropriate? \( \begin{array}{llll}\text { A } 1: 10000 & \text { B } 1: 20000 & \text { C } 1: 25000 & \text { D } 1: 50000\end{array} \)

We first convert the park’s dimensions from kilometers to centimeters. Since \[ 1\,\text{km} = 100\,000\,\text{cm}, \] the park’s dimensions in centimeters are: \[ \text{Length} = 10\,\text{km} = 10 \times 100\,000\,\text{cm} = 1\,000\,000\,\text{cm}, \] \[ \text{Width} = 6\,\text{km} = 6 \times 100\,000\,\text{cm} = 600\,000\,\text{cm}. \] Now, consider each proposed scale: 1. **Scale \(1:10000\):** The diagram dimensions are \[ \text{Length} = \frac{1\,000\,000\,\text{cm}}{10\,000} = 100\,\text{cm}, \] \[ \text{Width} = \frac{600\,000\,\text{cm}}{10\,000} = 60\,\text{cm}. \] These dimensions exceed the A3 paper size of \(42\,\text{cm}\) by \(29.7\,\text{cm}\) even if rotated. 2. **Scale \(1:20000\):** The diagram dimensions are \[ \text{Length} = \frac{1\,000\,000\,\text{cm}}{20\,000} = 50\,\text{cm}, \] \[ \text{Width} = \frac{600\,000\,\text{cm}}{20\,000} = 30\,\text{cm}. \] A length of \(50\,\text{cm}\) is still too long to fit on a \(42\,\text{cm}\) edge. 3. **Scale \(1:25000\):** The diagram dimensions are \[ \text{Length} = \frac{1\,000\,000\,\text{cm}}{25\,000} = 40\,\text{cm}, \] \[ \text{Width} = \frac{600\,000\,\text{cm}}{25\,000} = 24\,\text{cm}. \] Both \(40\,\text{cm}\) and \(24\,\text{cm}\) will fit well on an A3 sheet. 4. **Scale \(1:50000\):** The diagram dimensions are \[ \text{Length} = \frac{1\,000\,000\,\text{cm}}{50\,000} = 20\,\text{cm}, \] \[ \text{Width} = \frac{600\,000\,\text{cm}}{50\,000} = 12\,\text{cm}. \] While these dimensions would fit, the diagram would be very small and less useful. Thus, the most appropriate scale is \[ \boxed{1:25000}. \]