The area of the rubber coating for a flat roof is 96ft^2. The rectangular frame a carpenter built for the flat roof has dimensions such that the length is 4ft longer than the width. What are the dimensions of the farme?
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System of equations.
Have w=width, and l=length
w*l=96
l=w+4
w*(w+4)=96
w^2+4w=96
w^2+4w-96=0
(w+12)(w-8)=0
w=-12, w=8
Since only the positive one is reasonable in the context, it must be 8.
And since the length is 4ft longer than the width, it must be 12.
So length = 12 ft, width = 8 ft
Have w=width, and l=length
w*l=96
l=w+4
w*(w+4)=96
w^2+4w=96
w^2+4w-96=0
(w+12)(w-8)=0
w=-12, w=8
Since only the positive one is reasonable in the context, it must be 8.
And since the length is 4ft longer than the width, it must be 12.
So length = 12 ft, width = 8 ft
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w * l = 96
l = 4 + w
plug "4 + w" in for "l" in the first equation
w * (4 + w) = 96
distribute
4w + w² = 96
w² + 4w - 96 = 0
w² + 12w - 8w - 96 = 0
w(w+12) - 8(w+12) = 0
(w-8)(w+12) = 0
w - 8 = 0...or... w + 12 = 0
w = 8 ...or... w = -12
a dimension cannot be negative, so w = 8
plug 8 in for "w" in the second original equation.
l = 4 + 8
l = 12
The dimensions are 8 * 12
l = 4 + w
plug "4 + w" in for "l" in the first equation
w * (4 + w) = 96
distribute
4w + w² = 96
w² + 4w - 96 = 0
w² + 12w - 8w - 96 = 0
w(w+12) - 8(w+12) = 0
(w-8)(w+12) = 0
w - 8 = 0...or... w + 12 = 0
w = 8 ...or... w = -12
a dimension cannot be negative, so w = 8
plug 8 in for "w" in the second original equation.
l = 4 + 8
l = 12
The dimensions are 8 * 12
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maybe if you actually did your homework you could answer this..