SOLUTION: Bryan has 180 feet of fencing to fence off his rectangular garden. He will use the wall of his house as one side of the garden. Write an equation to find the area of the gar

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Bryan has 180 feet of fencing to fence off his rectangular garden. He will use the wall of his house as one side of the garden. Write an equation to find the area of the gar      Log On


   

Question 855293: Bryan has 180 feet of fencing to fence off his rectangular garden. He will use the wall of his house as one side of the garden.
Write an equation to find the area of the garden.
What dimensions create the garden with the greatest area?
What is the greatest area?
Answer by lwsshak3(11628) About Me  (Show Source):
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Bryan has 180 feet of fencing to fence off his rectangular garden. He will use the wall of his house as one side of the garden.
Write an equation to find the area of the garden.
What dimensions create the garden with the greatest area?
What is the greatest area?
***
Draw a rectangle with length of 2 sides at right angle to house=x
Length of side parallel to house=180-2x
..
Area=x(180-2x)=180x-2x^2
Area=-2x^2+180
complete the square:
Area=-2(x^2-90x+2025)+4050
Area=-2(x-45)^2+4050 (Equation for area of garden)
For maximum area:
x=45
180-2x=90
Dimensions that create the garden with the greatest area: 45 by 90 ft
Greatest area: 4050 sq ft