SOLUTION: After having a pool built in their backyard, the Harrisons have contracted to have a fence installed around the pool. They want to use 300 ft of fencing, and they plan to attatch t

Question 596351: After having a pool built in their backyard, the Harrisons have contracted to have a fence installed around the pool. They want to use 300 ft of fencing, and they plan to attatch the fence to the house. The Back of the house is 90 ft long, but they have instructed the fencing co. to use whatever portion of the house will maximize the area of the rectangular enclosure.
I know how to maximize the area, the only thing that is tripping me up is the fact that one side can be any value from the 90 ft side of the house. How do you set up an equation like that?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
After having a pool built in their backyard, the Harrisons have contracted to have a fence installed around the pool. They want to use 300 ft of fencing, and they plan to attatch the fence to the house. The Back of the house is 90 ft long, but they have instructed the fencing co. to use whatever portion of the house will maximize the area of the rectangular enclosure.
I know how to maximize the area, the only thing that is tripping me up is the fact that one side can be any value from the 90 ft side of the house. How do you set up an equation like that?
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The max area of a rectangle with one side fixed is having the long side 2x the short sides. That would be 75 by 150 in this case.
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Since the house is less than 150 ft, that will be one dimension of the rectangle.
--> 90 by 105 feet

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