A farmer wants to fence off a rectangular area of his property for his alpacas. In order to give the alpacas enough space he needs an area of 2700 square metres. One side of the area has to run along a road the remaining three slides are on his property. The cost for building a fancy fence along the road is $10 per metre, whereas the cost for building a much simpler fence along the remaining three sides that are on his property is only $6 per metre. The farmer wants to minimise the costs for fencing this area. What are the measurements of the rectangle for which the costs are minimised and what are the minimum costs? Clearly explain how you know that you have found the minimum costs. Remember to include units in your answer.