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Articles : Dividing Land Equally

Two brothers inherit land that they want to divide equally between them. The local land records indicate that the land is bounded roughly by the two functions:
8−​6​​x​2​​​​ and y=​10​​2​x−1​​​​−8, where x and y are measured in kilometers.
If they choose to put up a fence along a border running north and south, where should they put the fence?

1. Enter the functions in F1(X) and F2(X)
2. Use Plot or Numeric view to establish that the two boundaries intersect at x≈-9.8 and x≈7.2

3. Use Signed Area to estimate the area of the land to be 188.37 km² (18,837 hectares), so each brother should get approximately 94.185 km²

4. Optional: use Signed Area to get a visual estimation of the boundary

5. Define F3(X) as follows: F3(X)=∫​−9.8​X​​F1(T)−F2(T)δT
6. Use Plot view to get an estimate (x≈-0.7) and then use Numeric View to zoom in on the solution: x≈-0.644

Extensions:

• What if the brothers wanted an east-west boundary? Estimate where that boundary should be.
• The brothers want to divide the land into thirds; where do the north-south boundaries occur?

In this example, we used the Function app to easily visualize and estimate the solution to a typical classroom problem. In our next example, we extend that power of visualization.

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