Question 325595
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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.