A contractor is to fence off a rectangular field along a straight river, the side along the river requiring no fence. What is the greatest area the contractor can fence off using 500m of fencing?
The greatest area the contractor can fence off using 500m of fencing is a square with sides measuring 125m each.
To fence off a rectangular field along the river, the contractor will need to fence 3 sides of the field. This will consist of 2 sides measuring 125m each and 1 side measuring 250m. Therefore, the total fencing required will be 500m.
The area of a square with sides measuring 125m each is calculated as:
Area = side × side
Area = 125m × 125m
Area = 15625 m^2
Therefore, the greatest area the contractor can fence off is 15625 m^2.