Question 325595: Mrs. Thomas also has a garden in her yard and wants to put a 50-meter rectangular fence around it. She only needs to fence in 3 sides because the other side is alongside the house. the length The width of the garden is denoted by x, and by y.
A.Write an equation that would represent the fencing she would is using to enclose her garden using the given 50 meters. Write the equation as y in terms of x.(Solve for y)
B.Write an equation for the area, A, of the garden. Use your equation from Part A and write the Area equation in terms of (x).
C.If the area is 200 sq. meters, find the dimensions of the garden using your equation from Part B. You can use any of the methods you have learned in the course to solve your quadratic equation. Show all of your work.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! ..
Length of garden = x meters
width = y meters
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Let house be bordering one side of length.
So the fence required will be x+2y=50
add -x to both sides
x-x+2y=50-x
2y=50-x
divide by 2
2y/2 = 50-x / 2
y= 50-x /2...........A
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Area = xy
plug the value of y in the equation.
x*(50-x) / 2 = Area.............B
50x-x^2 /2 = 200
50x-x^2=400
x^2-50x+400=0
x^2-40x-10x+400=0
x(x-40)-10(x-40)=0
(x-10)(x-40)=0
x= 40 OR 10
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Plug the value of x in the equation y=50-x /2
suppose x=10 then y= 50-10 /2=20.
x=10,y=20
This does satisfy the value of area = 200.
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plug the value of x=40, 50-40 / 2= 5 meters
Length = 40 & width y = 5 xy= 200 = Area.
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