pen needs to be rectangular in shape however it will be built along a river side of the pen that does not need to be fenced. The farmer has a total of 700 feet of fence to build the pen. Determine the dimensions that will maximize area of the pen

Question

Mathematics

Nolan Mayer

10 March, 12:43

pen needs to be rectangular in shape however it will be built along a river side of the pen that does not need to be fenced. The farmer has a total of 700 feet of fence to build the pen. Determine the dimensions that will maximize area of the pen

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Skyler Mcintosh · Answer 1

Answer: The dimensions that will maximize area of the pen are 350 ft by 175 ft

Step-by-step explanation: The farmer has a total of 700 feet of fence for a rectangular pen which is in effect the perimeter. However, one side is by the river and would not need to be fenced. Hence we can determine that the perimeter would cover three sides only.

This means the sides would be in the ratio of 2 : 1 : 1

Hence, one side would be 2/4 and the other two sides would be 1/4 each

For the whole 700 meters of fencing, the sides can be calcualted as follows;

Length = 2/4 x 700

Length = 350

Width = 1/4 x 700

Width = 175

Therefore, with the length of fence available, the dimensions for the rectangular pen would be

Length = 350 ft

Width = 175 ft