Case Study Based Question There was a deserted land near Ryan's house. The colony people used to throw garbage on that land. Ryan, along with his friends, decided to develop the land into a park with walking track with uniform width, where children can play and elders can work. On the basis of above information answer the following questions: (a) What is the width of the track? (b) Find the breadth of inner rectangle. (c) Find the area of walking track. (d) Find the cost of leveling the park including the track at the rate 210 per square m . (e) Which values Ryan has shown here?

To determine the width of the track, breadth of the inner rectangle, area of the walking track, total cost of leveling, and the values Ryan demonstrated, follow these steps: 1. **Width of the Track (x):** - **Assumption:** Assume the outer rectangle has length (L) and breadth (B). - **Calculation:** \[ x = \frac{L - (L - 2x)}{2} = \frac{2x}{2} = x \] This indicates that without specific dimensions, the width cannot be determined numerically. 2. **Breadth of the Inner Rectangle (B_inner):** - **Calculation:** \[ B_{\text{inner}} = B - 2x \] Again, without specific values for B and x, the breadth cannot be calculated. 3. **Area of the Walking Track (A_track):** - **Calculation:** \[ A_{\text{track}} = L \times B - (L - 2x) \times (B - 2x) \] Simplifying: \[ A_{\text{track}} = 2xL + 2xB - 4x^2 \] Without specific values, the area cannot be determined. 4. **Cost of Leveling the Park:** - **Calculation:** \[ \text{Total Cost} = A_{\text{total}} \times 210 \] Or, if only the track area is leveled: \[ \text{Total Cost} = A_{\text{track}} \times 210 \] The exact cost depends on the total area to be leveled. 5. **Values Demonstrated by Ryan:** - **Practical Planning:** Ryan shows initiative in developing the land into a park. - **Geometric Understanding:** He considers the dimensions and areas involved. - **Financial Management:** Ryan accounts for the cost of leveling the park. - **Community Focus:** By creating a space for children to play and elders to work, Ryan demonstrates community-oriented values. **Conclusion:** Without specific numerical data, the exact values for the track width, inner rectangle breadth, walking track area, and total leveling cost cannot be determined. However, Ryan has demonstrated practical planning, geometric understanding, financial management, and community-oriented values in his project.