Answer:
width =4.5ft
length=6ft
Step-by-step explanation:
w = x
L = 2x-3
area = L*w
27 = x(2x-3)
[tex]27=2x^{2} -3x[/tex]
[tex]2x^{2} -3x-27=0[/tex]
[tex]2x^{2} +6x-9x-27=0[/tex]
2x(x+3)-9(x+3)=0
(2x-9)(x+3)=0
2x-9=0
2x=9
x=9/2
x=4.5
L=2x-3=2*4.5-3 =9-3=6
The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The length of the rectangle is 3ft less than twice the width.
Let width = x
Length = 2x - 3
The area of the rectangle = length × Width
27 = x(2x-3)
2x² - 3x = 27
2x² - 3x - 27 = 0
2x(x + 3) - 9(x + 3) = 0
(2x-9)(x+3)=0
The solutions are;
2x-9=0
2x=9
x=9/2
x = 4.5
(x+3) = 0
x = -3
The width cannot be negative.
So,
Length = 2x-3 = 2*4.5-3 = 9 - 3
Length = 6
Hence, The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
Learn more about the area;
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