Jim has 400 ft of fence material and needs to enclose an area of 10,000 square feet for his garden as the diagram depicts. (The length of the house is 62 ft, and the fence extends the same distance on either side of the house.) What must the dimensions of the rectangular enclosed region be? That is, what are the values of x and y? Round your answers to the nearest hundredth of a foot.Hello and thank you for posting your question to Brainmass.
The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.Feedback is always appreciated.The complete perimeter of the fence is:
the area is:
from equation (1.3) we have:
Plugging this back into equation (1.2):
(1.5)Multiplying both sides by x:
And we get the quadratic equation:
The roots are: (1.8)
Note that the equations are completely symmetric with respect to x and y, so we know that the equation for y will be identical to (1.7), that is it will be:
since the solution to this system of equation (and the dimensions of the fence) is:
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