Answer:
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
Step-by-step explanation:
Given that the shape of the shed is a rectangle, the expression for the area is:
[tex]A = w \cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the width and length of the shed, measured in feet. In addition, the statement shows that [tex]l = 2\cdot w - 3\,ft[/tex]. Then, the equation of area is expanded by replacing length:
[tex]A = w\cdot (2\cdot w - 3)[/tex]
[tex]A = 2\cdot w^{2} - 3\cdot w[/tex]
If [tex]A = 44\,ft^{2}[/tex], then, a second-order polynomial is formed:
[tex]2\cdot w^{2}-3\cdot w - 44 = 0[/tex]
The roots of this equation are found via General Equation for Second-Order Polynomials:
[tex]w_{1} = \frac{11}{2}\,ft[/tex] and [tex]w_{2} = -4\,ft[/tex]
Only the first roots is a physically reasonable solution. Then, the length of the shed is:
[tex]l = 2\cdot \left(\frac{11}{2}\,ft \right)-3\,ft[/tex]
[tex]l = 8\,ft[/tex]
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
